Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #22578128 | C2 | semidirect |
| 3. #22577756 | C2 | semidirect |
| 4. #22577701 | C2 | semidirect |
| 5. #22577685 | C2 | semidirect |
| 6. #22577624 | C2 | semidirect |
| 8. C8×Dic274 | C2 | semidirect |
| 9. C4×Dic548 | C2 | semidirect |
| 10. #22577494 | C2 | semidirect |
| 117. C137 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578139 | 2 |
| #22578128 | 2 |
| #22577756 | 2 |
| #22577701 | 2 |
| #22577685 | 2 |
| #22577624 | 2 |
| #22577600 | 2 |
| C8×Dic274 | 2 |
| C4×Dic548 | 2 |
| #22577494 | 2 |
| #486×C137 | 2 |
| #3365 | 137 |