Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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, prime radical, cosocle | C23×C29 | C24 |
| hypercenter | #391 | D29 |
| hypocenter | C29 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. #11745306 | C4 | semidirect |
| 57. C4×Dic29 | Q8 | semidirect |
| 97. Dic29 | C4×Q8 | semidirect |
| 98. Dic29 | C4⋊Q8 | semidirect |
| 133. C29 | C4×C4⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745306 | 2 |
| C2×Q8×Dic29 | 2 |
| C2×#11745249 | 2 |
| #14271069 | 2 |
| #14271060 | 2 |
| #14271032 | 2 |
| #14271014 | 2 |
| C42×Dic29 | 2 |
| C29×#391 | 2 |
| C4×C4⋊Q8 | 29 |