Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1056 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D29 |
| commutator, socle, cosocle | C23×C29 | C24 |
| Fitting | C29×#381 | C2 |
| hypercenter | #381 | D29 |
| hypocenter | C29 | #2404 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90805 | C2 | semidirect |
| 2. C2×#11745244 | C2 | semidirect |
| 3. C22×#90781 | C2 | semidirect |
| 4. #14271076 | C2 | semidirect |
| 5. #14271073 | C2 | semidirect |
| 6. #14271041 | C2 | semidirect |
| 7. #14271040 | C2 | semidirect |
| 8. C29×#381 | C2 | semidirect |
| 16. C22×D116 | C22 | semidirect |
| 17. C22×C4×D29 | C22 | semidirect |
| 18. C22×Dic58 | C22 | semidirect |
| 24. C2×#90781 | C22 | semidirect |
| 26. C29×#95 | C22 | semidirect |
| 27. C29×#95 | C22 | semidirect |
| 28. #11745179 | C22 | semidirect |
| 37. C22×C4×C29 | D4 | semidirect |
| 43. C2×C22⋊D29 | D4 | semidirect |
| 82. C22×D29 | #41 | semidirect |
| 134. #381 | D29 | semidirect |
| 160. #95 | C2×D29 | semidirect |
| 161. #95 | C2×D29 | semidirect |
| 162. C29 | #2404 | semidirect |
| 189. C22×C4 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745244 | 2 |
| C22×#90781 | 2 |
| #14271076 | 2 |
| #14271073 | 2 |
| #14271041 | 2 |
| #14271040 | 2 |
| C29×#381 | 2 |
| #2404 | 29 |