Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #22578139 | C2 | semidirect |
| 2. #22578114 | C2 | semidirect |
| 3. #22577756 | C2 | semidirect |
| 4. #22577705 | C2 | semidirect |
| 5. #22577695 | C2 | semidirect |
| 6. #22577617 | C2 | semidirect |
| 8. C8×Dic274 | C2 | semidirect |
| 9. C4×#14555499 | C2 | semidirect |
| 10. #22577483 | C2 | semidirect |
| 11. #486×C137 | C2 | semidirect |
| 122. C137 | #3361 | semidirect |
| 127. #486 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578139 | 2 |
| #22578114 | 2 |
| #22577756 | 2 |
| #22577705 | 2 |
| #22577695 | 2 |
| #22577617 | 2 |
| #22577595 | 2 |
| C8×Dic274 | 2 |
| C4×#14555499 | 2 |
| #22577483 | 2 |
| #486×C137 | 2 |
| #3361 | 137 |