Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D29 |
| commutator, cosocle | C16×C29 | C23 |
| Frattini | C16 | C22×D29 |
| Fitting | C29×SD64 | C2 |
| socle | C2×C29 | C2×D16 |
| hypercenter | SD64 | D29 |
| hypocenter | C29 | #2263 |
| LCS | G ▷ C16×C29 ▷ C8×C29 ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ SD64 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271596 | C2 | semidirect |
| 2. D16×D29 | C2 | semidirect |
| 3. #14271000 | C2 | semidirect |
| 4. D928 | C2 | semidirect |
| 5. #14270998 | C2 | semidirect |
| 6. #14270996 | C2 | semidirect |
| 7. C29×SD64 | C2 | semidirect |
| 10. C29×Q32 | C22 | semidirect |
| 15. D464 | C22 | semidirect |
| 17. C29×C32 | C22 | semidirect |
| 18. #11745142 | C22 | semidirect |
| 53. SD64 | D29 | semidirect |
| 64. Q32 | C2×D29 | semidirect |
| 72. C32 | C2×D29 | semidirect |
| 73. C29 | #2263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271596 | 2 |
| D16×D29 | 2 |
| #14271000 | 2 |
| D928 | 2 |
| #14270998 | 2 |
| #14270996 | 2 |
| C29×SD64 | 2 |
| #2263 | 29 |