Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
402 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 146 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. #22578436 | C2 | semidirect |
| 2. #22578434 | C2 | semidirect |
| 3. #22578433 | C2 | semidirect |
| 4. #22578430 | C2 | semidirect |
| 5. #22578423 | C2 | semidirect |
| 6. #22578420 | C2 | semidirect |
| 7. #22578377 | C2 | semidirect |
| 8. #22578376 | C2 | semidirect |
| 123. C137 | #2981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578436 | 2 |
| #22578434 | 2 |
| #22578433 | 2 |
| #22578430 | 2 |
| #22578423 | 2 |
| #22578420 | 2 |
| #22578377 | 2 |
| #22578376 | 2 |
| #22577948 | 2 |
| #2981 | 137 |