Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
472 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical, cosocle | C23×C29 | C24 |
| Fitting | C29×#384 | C2 |
| hypercenter | #384 | D29 |
| hypocenter | C29 | #2859 |
| LCS | G ▷ C23×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 64. C4×C29 | #125 | semidirect |
| 95. C29 | #2859 | semidirect |
| 143. C4 | #11745252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745252 | 2 |
| #14271062 | 2 |
| #14271059 | 2 |
| #14271033 | 2 |
| #14271028 | 2 |
| C42×Dic29 | 2 |
| C29×#384 | 2 |
| #2859 | 29 |