Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
2536 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 2536 conjugacy classes of subgroups — too many to draw. Only its 581 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×D29 |
| commutator, cosocle | C22×C29 | C25 |
| Frattini | C22 | C24×D29 |
| Fitting | C2×C29×#127 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C2×#127 | D29 |
| hypocenter | C29 | C2×D42 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D4×D29 | C2 | semidirect |
| 2. #14271798 | C2 | direct (N × H) |
| 3. C2×#11745300 | C2 | semidirect |
| 4. C2×#11745299 | C2 | semidirect |
| 5. C2×C4×D116 | C2 | semidirect |
| 6. C2×C29×#127 | C2 | semidirect |
| 7. C24×D29 | C22 | semidirect |
| 8. C22×D4×C29 | C22 | semidirect |
| 9. C22×D4×C29 | C22 | semidirect |
| 10. C22×C22⋊D29 | C22 | semidirect |
| 12. C2×D4×D29 | C22 | semidirect |
| 14. C22×C4×D29 | C22 | semidirect |
| 15. C29×#127 | C22 | semidirect |
| 16. C2×C42×C29 | C22 | semidirect |
| 17. C2×C22⋊Dic29 | C22 | semidirect |
| 18. #11745300 | C22 | semidirect |
| 19. #11745299 | C22 | semidirect |
| 20. C2×#90781 | C22 | semidirect |
| 21. C2×C4⋊Dic29 | C22 | semidirect |
| 22. C4×D116 | C22 | semidirect |
| 27. C23×D29 | C23 | semidirect |
| 30. C2×D4×C29 | C23 | semidirect |
| 31. C2×D4×C29 | C23 | semidirect |
| 35. C2×C22⋊D29 | C23 | semidirect |
| 38. C2×D116 | D4 | semidirect |
| 41. C2×C4×D29 | C23 | semidirect |
| 42. C42×C29 | C23 | semidirect |
| 43. C22⋊Dic29 | C23 | semidirect |
| 44. #90781 | C23 | semidirect |
| 45. C4⋊Dic29 | C23 | semidirect |
| 55. C22×D29 | C2×D4 | semidirect |
| 60. C2×C4×C29 | C2×D4 | semidirect |
| 66. D116 | C2×D4 | semidirect |
| 79. C2×D29 | C22×D4 | semidirect |
| 81. C4×C29 | C22×D4 | semidirect |
| 85. C2×#127 | D29 | semidirect |
| 90. C2×C29 | D42 | semidirect |
| 99. C22×D4 | C2×D29 | semidirect |
| 100. C22×D4 | C2×D29 | semidirect |
| 102. #127 | C2×D29 | semidirect |
| 109. C2×C42 | C2×D29 | semidirect |
| 110. C29 | C2×D42 | semidirect |
| 123. C2×D4 | C22×D29 | semidirect |
| 124. C2×D4 | C22×D29 | semidirect |
| 133. C42 | C22×D29 | semidirect |
| 153. C2×C4 | D4×D29 | semidirect |
| 169. C4 | C2×D4×D29 | semidirect |
| 172. C2 | #14271798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D29 | 2 |
| #14271798 | 2 |
| C2×#11745300 | 2 |
| C2×#11745299 | 2 |
| C2×C4×D116 | 2 |
| C2×C29×#127 | 2 |
| C2×D42 | 29 |