Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C22×C22⋊C4×C29 | C2 |
| hypercenter | C22×C22⋊C4 | D29 |
| hypocenter | C29 | #2404 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90805 | C2 | semidirect |
| 2. C2×#11745315 | C2 | semidirect |
| 3. #14271075 | C2 | semidirect |
| 4. #14271072 | C2 | semidirect |
| 5. #14271042 | C2 | semidirect |
| 6. #14271039 | C2 | semidirect |
| 7. #14271026 | C2 | semidirect |
| 8. C22×C22⋊C4×C29 | C2 | semidirect |
| 16. C22×D116 | C22 | semidirect |
| 17. C22×C4×D29 | C22 | semidirect |
| 18. C22×Dic58 | C22 | semidirect |
| 25. C2×#90781 | C22 | semidirect |
| 26. #11745179 | C22 | semidirect |
| 27. #11745179 | C22 | semidirect |
| 28. #11745179 | C22 | semidirect |
| 39. C22×C4×C29 | D4 | semidirect |
| 48. C2×C22⋊D29 | D4 | semidirect |
| 76. C23×C29 | #41 | semidirect |
| 129. C22×C22⋊C4 | D29 | semidirect |
| 162. C29 | #2404 | semidirect |
| 189. C22×C4 | C22⋊D29 | semidirect |
| 213. C23 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745315 | 2 |
| #14271075 | 2 |
| #14271072 | 2 |
| #14271042 | 2 |
| #14271039 | 2 |
| #14271026 | 2 |
| C22×C22⋊C4×C29 | 2 |
| #2404 | 29 |