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×#117 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C2×#117 | D29 |
| hypocenter | C29 | C2×#540 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271768 | C2 | direct (N × H) |
| 2. C2×#11745236 | C2 | semidirect |
| 3. C2×#11745232 | C2 | semidirect |
| 4. C2×#11745256 | C2 | semidirect |
| 5. C2×#11745292 | C2 | semidirect |
| 6. C2×#11745246 | C2 | semidirect |
| 7. C2×C4×D116 | C2 | semidirect |
| 8. C2×C29×#117 | C2 | semidirect |
| 14. C29×#117 | C22 | semidirect |
| 19. #11745292 | C22 | semidirect |
| 24. #11745256 | C22 | semidirect |
| 25. #11745246 | C22 | semidirect |
| 26. #11745236 | C22 | semidirect |
| 27. C4×D116 | C22 | semidirect |
| 28. #11745232 | C22 | semidirect |
| 100. C2×#117 | D29 | semidirect |
| 102. C2×C29 | #540 | semidirect |
| 117. #117 | C2×D29 | semidirect |
| 126. C29 | C2×#540 | semidirect |
| 192. C2 | #14271768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271768 | 2 |
| C2×#11745236 | 2 |
| C2×#11745232 | 2 |
| C2×#11745256 | 2 |
| C2×#11745292 | 2 |
| C2×#11745246 | 2 |
| C2×C4×D116 | 2 |
| C2×C29×#117 | 2 |
| C2×#540 | 29 |