Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×#393 | C2 |
| hypercenter | #393 | D29 |
| hypocenter | C29 | #2388 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#90809 | C2 | semidirect |
| 2. C2×#11745243 | C2 | semidirect |
| 3. #14271082 | C2 | semidirect |
| 4. #14271081 | C2 | semidirect |
| 5. #14271072 | C2 | semidirect |
| 6. #14271010 | C2 | semidirect |
| 7. C29×#393 | C2 | semidirect |
| 38. C2×C4×D29 | D4 | semidirect |
| 46. C23×C29 | #41 | semidirect |
| 64. C2×Dic29 | #41 | semidirect |
| 88. #393 | D29 | semidirect |
| 110. C29 | #2388 | semidirect |
| 140. C23 | #90809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C2×#11745243 | 2 |
| #14271082 | 2 |
| #14271081 | 2 |
| #14271072 | 2 |
| #14271010 | 2 |
| C29×#393 | 2 |
| #2388 | 29 |