Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 148 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. #22578438 | C2 | semidirect |
| 3. #22578434 | C2 | semidirect |
| 4. #22578434 | C2 | semidirect |
| 5. #22578427 | C2 | semidirect |
| 6. #22578423 | C2 | semidirect |
| 7. #22578367 | C2 | semidirect |
| 8. C4×#14555519 | C2 | semidirect |
| 111. C137 | #2967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578455 | 2 |
| #22578438 | 2 |
| #22578434 | 2 |
| #22578427 | 2 |
| #22578423 | 2 |
| #22578367 | 2 |
| C4×#14555519 | 2 |
| #22577934 | 2 |
| #2967 | 137 |