Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22577710 | C2 | semidirect |
| 3. #22577707 | C2 | semidirect |
| 6. #22577613 | C2 | semidirect |
| 7. #22577610 | C2 | semidirect |
| 94. C137 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578015 | 2 |
| #22577710 | 2 |
| #22577707 | 2 |
| #22577659 | 2 |
| #22577642 | 2 |
| #22577613 | 2 |
| #22577610 | 2 |
| #22577430 | 2 |
| #541×C137 | 2 |
| #3261 | 137 |