Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1058 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1058 conjugacy classes of subgroups — too many to draw. Only its 451 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 | C29×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D29 |
| hypocenter | C29 | #3529 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14271913 | C2 | semidirect |
| 2. #14271907 | C2 | semidirect |
| 3. #14271902 | C2 | semidirect |
| 4. #14271712 | C2 | semidirect |
| 5. #14271692 | C2 | semidirect |
| 6. #14271669 | C2 | semidirect |
| 7. C29×H(3,𝔽4) | C2 | semidirect |
| 8. C23×Dic29 | C22 | semidirect |
| 9. C2×#90809 | C22 | semidirect |
| 14. #11745315 | C22 | semidirect |
| 15. #11745308 | C22 | semidirect |
| 16. Q8×Dic29 | C22 | semidirect |
| 17. #11745306 | C22 | semidirect |
| 23. #11745248 | C22 | semidirect |
| 24. #11745246 | C22 | semidirect |
| 25. #11745245 | C22 | semidirect |
| 26. #11745243 | C22 | semidirect |
| 27. #11745241 | C22 | semidirect |
| 28. #11745240 | C22 | semidirect |
| 29. #11745239 | C22 | semidirect |
| 30. #11745237 | C22 | semidirect |
| 31. C42×D29 | C22 | semidirect |
| 32. #11745232 | C22 | semidirect |
| 96. H(3,𝔽4) | D29 | semidirect |
| 130. C29 | #3529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271913 | 2 |
| #14271907 | 2 |
| #14271902 | 2 |
| #14271712 | 2 |
| #14271692 | 2 |
| #14271669 | 2 |
| C29×H(3,𝔽4) | 2 |
| #3529 | 29 |