Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Frattini | C22 | C24×D29 |
| Fitting | C22×C42×C29 | C2 |
| hypercenter | C22×C42 | D29 |
| hypocenter | C29 | #3444 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271720 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. #14271697 | C2 | semidirect |
| 4. #14271674 | C2 | semidirect |
| 5. C4×#90805 | C2 | semidirect |
| 6. C22×C42×C29 | C2 | semidirect |
| 18. #11745238 | C22 | semidirect |
| 19. #11745237 | C22 | semidirect |
| 20. #11745236 | C22 | semidirect |
| 21. C4×D116 | C22 | semidirect |
| 22. #11745234 | C22 | semidirect |
| 23. C42×D29 | C22 | semidirect |
| 24. #11745232 | C22 | semidirect |
| 25. #11745231 | C22 | semidirect |
| 26. C4×Dic58 | C22 | semidirect |
| 55. C2×C4×C29 | #41 | semidirect |
| 79. C22×C42 | D29 | semidirect |
| 103. C29 | #3444 | semidirect |
| 137. C2×C4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271720 | 2 |
| #14271713 | 2 |
| #14271697 | 2 |
| #14271674 | 2 |
| C4×#90805 | 2 |
| C22×C42×C29 | 2 |
| #3444 | 29 |