Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
364 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 1. #22578455 | C2 | semidirect |
| 2. #22578454 | C2 | semidirect |
| 3. #22578452 | C2 | semidirect |
| 98. C137 | #2984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578455 | 2 |
| #22578454 | 2 |
| #22578452 | 2 |
| #22578426 | 2 |
| #22578425 | 2 |
| #22578422 | 2 |
| #22578421 | 2 |
| C4×Q8×D137 | 2 |
| #2984 | 137 |