Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C22×C29 | C23×C4 |
| Fitting | C29×#391 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C23×D29 | C23 |
| hypercenter | #391 | D29 |
| hypocenter | C29 | #2310 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14271070 | C2 | semidirect |
| 5. #14271069 | C2 | semidirect |
| 6. #14271068 | C2 | semidirect |
| 7. #14271067 | C2 | semidirect |
| 9. C29×#391 | C2 | semidirect |
| 13. C2×Q8×D29 | C4 | semidirect |
| 124. #391 | D29 | semidirect |
| 154. C29 | #2310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D29 | 2 |
| C2×#11745254 | 2 |
| C2×#11745234 | 2 |
| #14271070 | 2 |
| #14271069 | 2 |
| #14271068 | 2 |
| #14271067 | 2 |
| #14271025 | 2 |
| C29×#391 | 2 |
| #2310 | 29 |