Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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×#540 |
| 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. #14271767 | C2 | direct (N × H) |
| 2. C2×#11745232 | C2 | semidirect |
| 3. C2×#11745297 | C2 | semidirect |
| 4. C2×#11745301 | C2 | semidirect |
| 5. C2×#11745300 | C2 | semidirect |
| 6. C2×D4×Dic29 | C2 | semidirect |
| 7. C2×#11745234 | C2 | semidirect |
| 8. C2×C29×#127 | C2 | semidirect |
| 14. C29×#127 | C22 | semidirect |
| 18. #11745301 | C22 | semidirect |
| 19. #11745300 | C22 | semidirect |
| 20. #11745297 | C22 | semidirect |
| 21. D4×Dic29 | C22 | semidirect |
| 27. #11745234 | C22 | semidirect |
| 28. #11745232 | C22 | semidirect |
| 94. C2×#127 | D29 | semidirect |
| 102. C2×C29 | #540 | semidirect |
| 111. #127 | C2×D29 | semidirect |
| 126. C29 | C2×#540 | semidirect |
| 192. C2 | #14271767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271767 | 2 |
| C2×#11745232 | 2 |
| C2×#11745297 | 2 |
| C2×#11745301 | 2 |
| C2×#11745300 | 2 |
| C2×D4×Dic29 | 2 |
| C2×#11745234 | 2 |
| C2×C29×#127 | 2 |
| C2×#540 | 29 |