Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#17984111 | C2 | semidirect |
| 2. #22577954 | C2 | semidirect |
| 3. C4×#14555511 | C2 | semidirect |
| 4. #22577627 | C2 | semidirect |
| 5. #22577621 | C2 | semidirect |
| 6. #22577605 | C2 | semidirect |
| 7. #22577603 | C2 | semidirect |
| 8. #22577599 | C2 | semidirect |
| 9. C4⋊C8×D137 | C2 | semidirect |
| 10. #22577398 | C2 | semidirect |
| 11. #462×C137 | C2 | semidirect |
| 47. #14555511 | D4 | semidirect |
| 137. C4×C137 | #135 | semidirect |
| 150. C137 | #3035 | semidirect |
| 157. #462 | D137 | semidirect |
| 292. C4 | #17984111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984111 | 2 |
| #22577954 | 2 |
| C4×#14555511 | 2 |
| #22577627 | 2 |
| #22577621 | 2 |
| #22577605 | 2 |
| #22577603 | 2 |
| #22577599 | 2 |
| C4⋊C8×D137 | 2 |
| #22577398 | 2 |
| #462×C137 | 2 |
| #3035 | 137 |