Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
588 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 249 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×#384 | C2 |
| socle, prime radical, cosocle | C23×C29 | C24 |
| hypercenter | #384 | D29 |
| hypocenter | C29 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 20. #11745231 | C4 | semidirect |
| 41. C4×Dic29 | Q8 | semidirect |
| 70. C4×C29 | C4×Q8 | semidirect |
| 74. Dic29 | C4⋊Q8 | semidirect |
| 101. C29 | C4×C4⋊Q8 | semidirect |
| 152. C4 | #11745249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745231 | 2 |
| C2×#11745249 | 2 |
| #14271068 | 2 |
| #14271059 | 2 |
| C4⋊C4×Dic29 | 2 |
| C42×Dic29 | 2 |
| C29×#384 | 2 |
| C4×C4⋊Q8 | 29 |