Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D29 |
| commutator, socle, cosocle | C22×C29 | C25 |
| Fitting | C23×Q8×C29 | C2 |
| hypercenter | C23×Q8 | D29 |
| hypocenter | C29 | #3486 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745362 | C2 | semidirect |
| 2. Q8×C22⋊D29 | C2 | semidirect |
| 3. #14271824 | C2 | semidirect |
| 4. #14271737 | C2 | semidirect |
| 5. #14271674 | C2 | semidirect |
| 6. #14271641 | C2 | semidirect |
| 7. C23×Q8×C29 | C2 | semidirect |
| 14. C2×#90809 | C22 | semidirect |
| 15. C2×Q8×D29 | C22 | semidirect |
| 18. #11745309 | C22 | semidirect |
| 19. #11745308 | C22 | semidirect |
| 20. Q8×Dic29 | C22 | semidirect |
| 21. #11745306 | C22 | semidirect |
| 30. C2×Q8×C29 | D4 | semidirect |
| 76. C22×C29 | 2−1+4 | semidirect |
| 85. C23×Q8 | D29 | semidirect |
| 115. C29 | #3486 | semidirect |
| 123. C2×Q8 | C22⋊D29 | semidirect |
| 165. C22 | #11745362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| Q8×C22⋊D29 | 2 |
| #14271824 | 2 |
| #14271737 | 2 |
| #14271674 | 2 |
| #14271641 | 2 |
| C23×Q8×C29 | 2 |
| #3486 | 29 |