Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
432 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 139 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×D137 |
| commutator, socle, cosocle | C23×C137 | C24 |
| Fitting | #396×C137 | C2 |
| prime radical | C24×C137 | C23 |
| hypercenter | #396 | D137 |
| hypocenter | C137 | #2401 |
| LCS | G ▷ C23×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C137⋊#401 | C2 | semidirect |
| 2. #22577342 | C2 | semidirect |
| 4. C4⋊C4×Dic137 | C2 | semidirect |
| 6. #22577248 | C2 | semidirect |
| 70. C137 | #2401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C137⋊#401 | 2 |
| #22577342 | 2 |
| #22577328 | 2 |
| C4⋊C4×Dic137 | 2 |
| C22⋊C4×Dic137 | 2 |
| #22577248 | 2 |
| #396×C137 | 2 |
| #2401 | 137 |