Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #22578245 | C2 | semidirect |
| 4. #22578245 | C2 | semidirect |
| 5. #22578244 | C2 | semidirect |
| 6. C8×#11764047 | C2 | semidirect |
| 72. C137 | #1454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578422 | 2 |
| #22578421 | 2 |
| #22578245 | 2 |
| #22578244 | 2 |
| C8×#11764047 | 2 |
| #22577455 | 2 |
| #1454 | 137 |