Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
944 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 167 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×#392 | C2 |
| hypercenter | #392 | D29 |
| hypocenter | C29 | #2388 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90807 | C2 | semidirect |
| 2. C2×D4×Dic29 | C2 | semidirect |
| 3. C2×#11745243 | C2 | semidirect |
| 4. #14271084 | C2 | semidirect |
| 5. #14271079 | C2 | semidirect |
| 6. #14271077 | C2 | semidirect |
| 7. #14271075 | C2 | semidirect |
| 8. #14271071 | C2 | semidirect |
| 9. C22⋊C4×Dic29 | C2 | semidirect |
| 10. #14271010 | C2 | semidirect |
| 11. C29×#392 | C2 | semidirect |
| 60. C22×Dic29 | D4 | semidirect |
| 68. C2×C4×D29 | D4 | semidirect |
| 93. C23×C29 | #41 | semidirect |
| 108. C2×C4×C29 | #41 | semidirect |
| 125. C2×Dic29 | #41 | semidirect |
| 167. #392 | D29 | semidirect |
| 205. C29 | #2388 | semidirect |
| 265. C23 | #90807 | semidirect |
| 294. C2×C4 | #90807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90807 | 2 |
| C2×D4×Dic29 | 2 |
| C2×#11745243 | 2 |
| #14271084 | 2 |
| #14271079 | 2 |
| #14271077 | 2 |
| #14271075 | 2 |
| #14271071 | 2 |
| C22⋊C4×Dic29 | 2 |
| #14271010 | 2 |
| C29×#392 | 2 |
| #2388 | 29 |