Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1152 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 469 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×#125 | C2 |
| socle | C23×C29 | C24 |
| hypercenter | C2×#125 | D29 |
| hypocenter | C29 | C2×#562 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271911 | C2 | direct (N × H) |
| 2. C2×#11745237 | C2 | semidirect |
| 3. C2×#11745256 | C2 | semidirect |
| 4. C2×#11745258 | C2 | semidirect |
| 5. C2×#11745257 | C2 | semidirect |
| 6. C2×C29×#125 | C2 | semidirect |
| 11. C29×#125 | C22 | semidirect |
| 19. #11745258 | C22 | semidirect |
| 20. #11745257 | C22 | semidirect |
| 21. #11745256 | C22 | semidirect |
| 22. #11745237 | C22 | semidirect |
| 73. C2×#125 | D29 | semidirect |
| 78. C2×C29 | #562 | semidirect |
| 86. #125 | C2×D29 | semidirect |
| 98. C29 | C2×#562 | semidirect |
| 148. C2 | #14271911 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271911 | 2 |
| C2×#11745237 | 2 |
| C2×#11745256 | 2 |
| C2×#11745258 | 2 |
| C2×#11745257 | 2 |
| C2×C29×#125 | 2 |
| C2×#562 | 29 |