Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
672 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 189 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×#379 | C2 |
| socle, cosocle | C23×C29 | C24 |
| prime radical | C25×C29 | C22 |
| hypercenter | #379 | D29 |
| hypocenter | C29 | #2312 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14271057 | C2 | semidirect |
| 3. #14271051 | C2 | semidirect |
| 4. #14271021 | C2 | semidirect |
| 6. C22⋊C4×Dic29 | C2 | semidirect |
| 14. C2×C22⋊Dic29 | C4 | semidirect |
| 20. C2×#90779 | C22 | semidirect |
| 21. C2×C4×Dic29 | C22 | semidirect |
| 22. #11745179 | C22 | semidirect |
| 23. #11745179 | C22 | semidirect |
| 130. C29 | #2312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic29 | 2 |
| #14271057 | 2 |
| #14271051 | 2 |
| #14271021 | 2 |
| #14271019 | 2 |
| C22⋊C4×Dic29 | 2 |
| C29×#379 | 2 |
| #2312 | 29 |