Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #22577882 | C2 | semidirect |
| 3. #22577515 | C2 | semidirect |
| 4. #22577511 | C2 | semidirect |
| 5. #22577509 | C2 | semidirect |
| 6. #22577494 | C2 | semidirect |
| 7. C4×#14555498 | C2 | semidirect |
| 8. #106×D137 | C2 | semidirect |
| 9. #22577401 | C2 | semidirect |
| 10. #22577360 | C2 | semidirect |
| 11. #442×C137 | C2 | semidirect |
| 13. #17984107 | C4 | semidirect |
| 41. #14555509 | C2×C4 | semidirect |
| 48. Dic548 | C2×C4 | semidirect |
| 49. #14555498 | C2×C4 | semidirect |
| 53. C8×D137 | C2×C4 | semidirect |
| 66. D8×C137 | C2×C4 | semidirect |
| 114. C137 | #2952 | semidirect |
| 119. #442 | D137 | semidirect |
| 167. D8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984107 | 2 |
| #22577882 | 2 |
| #22577515 | 2 |
| #22577511 | 2 |
| #22577509 | 2 |
| #22577494 | 2 |
| C4×#14555498 | 2 |
| #106×D137 | 2 |
| #22577401 | 2 |
| #22577360 | 2 |
| #442×C137 | 2 |
| #2952 | 137 |