Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #22578127 | C2 | semidirect |
| 3. #22577725 | C2 | semidirect |
| 4. #22577685 | C2 | semidirect |
| 5. #22577631 | C2 | semidirect |
| 6. #22577600 | C2 | semidirect |
| 7. #22577566 | C2 | semidirect |
| 8. C4×Dic548 | C2 | semidirect |
| 9. C8×D548 | C2 | semidirect |
| 10. #22577396 | C2 | semidirect |
| 11. #486×C137 | C2 | semidirect |
| 127. C137 | #3304 | semidirect |
| 131. #486 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578127 | 2 |
| #22578073 | 2 |
| #22577725 | 2 |
| #22577685 | 2 |
| #22577631 | 2 |
| #22577600 | 2 |
| #22577566 | 2 |
| C4×Dic548 | 2 |
| C8×D548 | 2 |
| #22577396 | 2 |
| #486×C137 | 2 |
| #3304 | 137 |