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. #22577885 | C2 | semidirect |
| 3. #22577516 | C2 | semidirect |
| 4. #22577514 | C2 | semidirect |
| 5. #22577510 | C2 | semidirect |
| 6. C4×#14555497 | C2 | semidirect |
| 7. #22577488 | C2 | semidirect |
| 8. #106×D137 | C2 | semidirect |
| 9. #22577403 | C2 | semidirect |
| 10. #22577360 | C2 | semidirect |
| 11. #441×C137 | C2 | semidirect |
| 13. #17984111 | C4 | semidirect |
| 41. #14555511 | C2×C4 | semidirect |
| 49. #14555497 | C2×C4 | semidirect |
| 50. D1096 | C2×C4 | semidirect |
| 54. C8×D137 | C2×C4 | semidirect |
| 65. Q16×C137 | C2×C4 | semidirect |
| 114. C137 | #2952 | semidirect |
| 121. #441 | D137 | semidirect |
| 165. Q16 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984111 | 2 |
| #22577885 | 2 |
| #22577516 | 2 |
| #22577514 | 2 |
| #22577510 | 2 |
| C4×#14555497 | 2 |
| #22577488 | 2 |
| #106×D137 | 2 |
| #22577403 | 2 |
| #22577360 | 2 |
| #441×C137 | 2 |
| #2952 | 137 |