Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C22×#41×C29 | C2 |
| hypercenter | C22×#41 | D29 |
| hypocenter | C29 | #3487 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745362 | C2 | semidirect |
| 2. #14271832 | C2 | semidirect |
| 3. #14271820 | C2 | semidirect |
| 4. #14271730 | C2 | semidirect |
| 5. #14271674 | C2 | semidirect |
| 6. #14271641 | C2 | semidirect |
| 7. C22×#41×C29 | C2 | semidirect |
| 14. C2×#90809 | C22 | semidirect |
| 15. C2×Q8×D29 | C22 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 19. #11745302 | C22 | semidirect |
| 20. #11745300 | C22 | semidirect |
| 21. #11745298 | C22 | semidirect |
| 22. #11745292 | C22 | semidirect |
| 24. C4×C22⋊D29 | C22 | semidirect |
| 26. #11745286 | C22 | semidirect |
| 29. C2×Q8×C29 | D4 | semidirect |
| 84. C22×#41 | D29 | semidirect |
| 114. C29 | #3487 | semidirect |
| 121. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| #14271832 | 2 |
| #14271820 | 2 |
| #14271730 | 2 |
| #14271674 | 2 |
| #14271641 | 2 |
| C22×#41×C29 | 2 |
| #3487 | 29 |