Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578128 | C2 | semidirect |
| 3. #22577752 | C2 | semidirect |
| 4. #22577686 | C2 | semidirect |
| 5. #22577685 | C2 | semidirect |
| 8. C8×Dic274 | C2 | semidirect |
| 11. #487×C137 | C2 | semidirect |
| 78. Dic274 | SD16 | semidirect |
| 118. C137 | #3359 | semidirect |
| 123. #487 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578128 | 2 |
| #22578068 | 2 |
| #22577752 | 2 |
| #22577686 | 2 |
| #22577685 | 2 |
| #22577607 | 2 |
| #22577605 | 2 |
| C8×Dic274 | 2 |
| C4×#14555499 | 2 |
| #22577488 | 2 |
| #487×C137 | 2 |
| #3359 | 137 |