Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 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. #22578068 | C2 | semidirect |
| 3. #22577753 | C2 | semidirect |
| 4. #22577732 | C2 | semidirect |
| 5. #22577689 | C2 | semidirect |
| 6. #22577629 | C2 | semidirect |
| 7. #22577540 | C2 | semidirect |
| 8. C4×#14555498 | C2 | semidirect |
| 9. #22577468 | C2 | semidirect |
| 10. #103×D137 | C2 | semidirect |
| 11. #461×C137 | C2 | semidirect |
| 81. Dic274 | #41 | semidirect |
| 82. D548 | SD16 | semidirect |
| 128. C137 | #3298 | semidirect |
| 136. #461 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578068 | 2 |
| #22578058 | 2 |
| #22577753 | 2 |
| #22577732 | 2 |
| #22577689 | 2 |
| #22577629 | 2 |
| #22577540 | 2 |
| C4×#14555498 | 2 |
| #22577468 | 2 |
| #103×D137 | 2 |
| #461×C137 | 2 |
| #3298 | 137 |