Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 1. #22578127 | C2 | semidirect |
| 3. #22577740 | C2 | semidirect |
| 4. #22577730 | C2 | semidirect |
| 5. #22577685 | C2 | semidirect |
| 6. #22577680 | C2 | semidirect |
| 7. #22577650 | C2 | semidirect |
| 8. C4×#14555499 | C2 | semidirect |
| 9. #22577482 | C2 | semidirect |
| 10. #22577444 | C2 | semidirect |
| 11. #500×C137 | C2 | semidirect |
| 99. C8×C137 | #41 | semidirect |
| 122. C137 | #3353 | semidirect |
| 126. #500 | D137 | semidirect |
| 222. C8 | #14555511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578127 | 2 |
| #22578056 | 2 |
| #22577740 | 2 |
| #22577730 | 2 |
| #22577685 | 2 |
| #22577680 | 2 |
| #22577650 | 2 |
| C4×#14555499 | 2 |
| #22577482 | 2 |
| #22577444 | 2 |
| #500×C137 | 2 |
| #3353 | 137 |