Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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×#532 |
| 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×#90807 | C2 | semidirect |
| 2. #14271711 | C2 | direct (N × H) |
| 3. C2×#11745231 | C2 | semidirect |
| 4. C2×#11745298 | C2 | semidirect |
| 5. C2×#11745300 | C2 | semidirect |
| 6. C2×D4×Dic29 | C2 | semidirect |
| 7. C2×C42×D29 | C2 | semidirect |
| 8. C2×C29×#127 | C2 | semidirect |
| 14. C2×#90807 | C22 | semidirect |
| 18. C29×#127 | C22 | semidirect |
| 21. #11745300 | C22 | semidirect |
| 22. #11745298 | C22 | semidirect |
| 23. D4×Dic29 | C22 | semidirect |
| 27. C42×D29 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 46. C2×C4×D29 | D4 | semidirect |
| 66. C2×C4×C29 | #41 | semidirect |
| 78. C4×D29 | C2×D4 | semidirect |
| 91. C4×C29 | C2×#41 | semidirect |
| 98. C2×#127 | D29 | semidirect |
| 104. C2×C29 | #532 | semidirect |
| 118. #127 | C2×D29 | semidirect |
| 128. C29 | C2×#532 | semidirect |
| 177. C2×C4 | #90807 | semidirect |
| 193. C4 | C2×#90807 | semidirect |
| 196. C2 | #14271711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| #14271711 | 2 |
| C2×#11745231 | 2 |
| C2×#11745298 | 2 |
| C2×#11745300 | 2 |
| C2×D4×Dic29 | 2 |
| C2×C42×D29 | 2 |
| C2×C29×#127 | 2 |
| C2×#532 | 29 |