Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D73 |
| commutator | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | C2×#120×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C2×#120 | D73 |
| hypocenter | C73 | C22×#120 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D73 | C2 | semidirect |
| 2. C22×D4×D73 | C2 | semidirect |
| 3. C2×#14556561 | C2 | semidirect |
| 4. C2×#14556560 | C2 | semidirect |
| 5. C2×#14556559 | C2 | semidirect |
| 6. #120×D73 | C2 | direct (N × H) |
| 7. C2×C22⋊C4×D73 | C2 | semidirect |
| 8. C2×#120×C73 | C2 | semidirect |
| 11. C24×D73 | C22 | semidirect |
| 12. C24×D73 | C22 | semidirect |
| 13. C24×D73 | C22 | semidirect |
| 14. C22×D292 | C22 | semidirect |
| 15. C22×C22⋊D73 | C22 | semidirect |
| 16. C22×C22⋊D73 | C22 | semidirect |
| 18. C2×D4×D73 | C22 | semidirect |
| 19. C22×C4×D73 | C22 | semidirect |
| 20. #14556561 | C22 | semidirect |
| 21. #14556560 | C22 | semidirect |
| 22. #14556559 | C22 | semidirect |
| 23. C2×C22⋊Dic73 | C22 | semidirect |
| 24. C2×#11924005 | C22 | semidirect |
| 25. C22⋊C4×D73 | C22 | semidirect |
| 26. C25×C73 | C22 | semidirect |
| 27. C22×D4×C73 | C22 | semidirect |
| 28. #120×C73 | C22 | semidirect |
| 29. C2×C22⋊C4×C73 | C22 | semidirect |
| 36. C23×D73 | D4 | semidirect |
| 40. C23×D73 | C23 | semidirect |
| 41. C23×D73 | C23 | semidirect |
| 42. C23×D73 | C23 | semidirect |
| 44. C2×D292 | C23 | semidirect |
| 47. C2×C22⋊D73 | C23 | semidirect |
| 48. C2×C22⋊D73 | C23 | semidirect |
| 50. C22×Dic73 | C23 | semidirect |
| 52. C2×C4×D73 | C23 | semidirect |
| 53. C22⋊Dic73 | C23 | semidirect |
| 54. #11924005 | C23 | semidirect |
| 57. C24×C73 | C23 | semidirect |
| 58. C24×C73 | C23 | semidirect |
| 60. C2×D4×C73 | C23 | semidirect |
| 61. C22×C4×C73 | C23 | semidirect |
| 62. C22⋊C4×C73 | C23 | semidirect |
| 67. C23×C73 | C2×D4 | semidirect |
| 70. C23×C73 | C24 | semidirect |
| 82. C22×D73 | C2×D4 | semidirect |
| 83. C22×D73 | C2×D4 | semidirect |
| 86. C22×D73 | C24 | semidirect |
| 89. C2×C4×C73 | C24 | semidirect |
| 93. C2×Dic73 | C24 | semidirect |
| 102. C22×C73 | C22×D4 | semidirect |
| 111. C2×D73 | #120 | direct (N × H) |
| 113. C2×D73 | C22×D4 | semidirect |
| 118. C2×C73 | C2×#120 | semidirect |
| 122. D73 | C2×#120 | direct (N × H) |
| 124. C73 | C22×#120 | semidirect |
| 131. C2×#120 | D73 | direct (N × H) |
| 138. C25 | C2×D73 | semidirect |
| 144. C22×D4 | C2×D73 | semidirect |
| 149. #120 | C2×D73 | direct (N × H) |
| 153. C2×C22⋊C4 | C2×D73 | semidirect |
| 169. C24 | C22×D73 | semidirect |
| 170. C24 | C22×D73 | semidirect |
| 179. C2×D4 | C22×D73 | semidirect |
| 183. C22×C4 | C22×D73 | semidirect |
| 186. C22⋊C4 | C22×D73 | semidirect |
| 207. C23 | D4×D73 | semidirect |
| 210. C23 | C23×D73 | semidirect |
| 219. C2×C4 | C23×D73 | semidirect |
| 236. C22 | C2×D4×D73 | semidirect |
| 245. C2 | #120×D73 | direct (N × H) |