Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
420 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 139 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. D4×Dic274 | C2 | semidirect |
| 3. #22577754 | C2 | semidirect |
| 4. #22577734 | C2 | semidirect |
| 5. #22577689 | C2 | semidirect |
| 6. #22577632 | C2 | semidirect |
| 7. #22577609 | C2 | semidirect |
| 8. #22577544 | C2 | semidirect |
| 9. C4×#14555499 | C2 | semidirect |
| 10. C2×#17984013 | C2 | semidirect |
| 11. C8×D4×C137 | C2 | semidirect |
| 83. Dic274 | #41 | semidirect |
| 96. D4×C137 | SD16 | semidirect |
| 128. C137 | #3298 | semidirect |
| 139. C8×D4 | D137 | semidirect |
| 217. D4 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic274 | 2 |
| #22578057 | 2 |
| #22577754 | 2 |
| #22577734 | 2 |
| #22577689 | 2 |
| #22577632 | 2 |
| #22577609 | 2 |
| #22577544 | 2 |
| C4×#14555499 | 2 |
| C2×#17984013 | 2 |
| C8×D4×C137 | 2 |
| #3298 | 137 |