Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#64408 |
| commutator | C2×C73 | C24×C4 |
| Frattini | C2 | C24×#64408 |
| Fitting | C22×D4×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C22×D4 | #64408 |
| hypocenter | C73 | C22×C4×D4 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#64408 | C2 | semidirect |
| 2. C2×D4×#64408 | C2 | direct (N × H) |
| 3. C22×C4⋊#64408 | C2 | semidirect |
| 4. C22×C22⋊#64408 | C2 | semidirect |
| 5. C22×C4×#64408 | C2 | semidirect |
| 11. C23×#64408 | C22 | semidirect |
| 12. D4×#64408 | C22 | direct (N × H) |
| 13. C2×C4⋊#64408 | C22 | semidirect |
| 14. C2×C22⋊#64408 | C22 | semidirect |
| 15. C2×C4×#64408 | C22 | semidirect |
| 17. C22×D292 | C4 | semidirect |
| 18. C22×C22⋊D73 | C4 | semidirect |
| 19. C2×D4×D73 | C4 | semidirect |
| 22. C22×D4×C73 | C4 | semidirect |
| 26. C22×#64408 | D4 | direct (N × H) |
| 30. C22×#64408 | C23 | semidirect |
| 31. C4⋊#64408 | C23 | semidirect |
| 32. C22⋊#64408 | C23 | semidirect |
| 33. C4×#64408 | C23 | semidirect |
| 36. C23×D73 | C2×C4 | semidirect |
| 37. C23×D73 | C2×C4 | semidirect |
| 40. C2×D292 | C2×C4 | semidirect |
| 41. C2×C22⋊D73 | C2×C4 | semidirect |
| 42. D4×D73 | C2×C4 | semidirect |
| 44. C22×Dic73 | C2×C4 | semidirect |
| 45. C2×C4×D73 | C2×C4 | semidirect |
| 47. C24×C73 | C2×C4 | semidirect |
| 48. C2×D4×C73 | C2×C4 | semidirect |
| 49. C22×C4×C73 | C2×C4 | semidirect |
| 52. C23×C73 | C22×C4 | semidirect |
| 58. C22×D73 | C22×C4 | semidirect |
| 59. C22×D73 | C22×C4 | semidirect |
| 67. C2×#64408 | C2×D4 | direct (N × H) |
| 71. D4×C73 | C22×C4 | semidirect |
| 72. C2×C4×C73 | C22×C4 | semidirect |
| 73. C22⋊D73 | C22×C4 | semidirect |
| 74. C2×Dic73 | C22×C4 | semidirect |
| 75. D292 | C22×C4 | semidirect |
| 76. C4×D73 | C22×C4 | semidirect |
| 79. C22×C73 | C4×D4 | semidirect |
| 81. C22×C73 | C23×C4 | semidirect |
| 86. C2×D73 | C4×D4 | semidirect |
| 88. C2×D73 | C23×C4 | semidirect |
| 94. #64408 | C22×D4 | direct (N × H) |
| 95. C4×C73 | C23×C4 | semidirect |
| 96. Dic73 | C23×C4 | semidirect |
| 98. C2×C73 | C2×C4×D4 | semidirect |
| 101. D73 | C2×C4×D4 | semidirect |
| 105. C73 | C22×C4×D4 | semidirect |
| 117. C22×D4 | #64408 | direct (N × H) |
| 134. C24 | C2×#64408 | semidirect |
| 139. C2×D4 | C2×#64408 | direct (N × H) |
| 151. C22×C4 | C2×#64408 | semidirect |
| 168. C23 | C22×#64408 | semidirect |
| 171. D4 | C22×#64408 | direct (N × H) |
| 182. C2×C4 | C22×#64408 | semidirect |
| 194. C22 | D4×#64408 | direct (N × H) |
| 196. C22 | C23×#64408 | semidirect |
| 201. C4 | C23×#64408 | semidirect |
| 207. C2 | C2×D4×#64408 | direct (N × H) |