Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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×#394 | C2 |
| prime radical | C22×D4×C29 | C22 |
| hypercenter | #394 | D29 |
| hypocenter | C29 | #2398 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745249 | C2 | semidirect |
| 3. #14271103 | C2 | semidirect |
| 4. #14271102 | C2 | semidirect |
| 5. #14271091 | C2 | semidirect |
| 7. #14271075 | C2 | semidirect |
| 8. C22⋊C4×Dic29 | C2 | semidirect |
| 9. C22⋊C4×Dic29 | C2 | semidirect |
| 10. #14271008 | C2 | semidirect |
| 171. C29 | #2398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745249 | 2 |
| C2×D4×Dic29 | 2 |
| #14271103 | 2 |
| #14271102 | 2 |
| #14271091 | 2 |
| #14271077 | 2 |
| #14271075 | 2 |
| C22⋊C4×Dic29 | 2 |
| #14271008 | 2 |
| C29×#394 | 2 |
| #2398 | 29 |