Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984094 | C2 | semidirect |
| 2. #22577970 | C2 | semidirect |
| 3. #22577653 | C2 | semidirect |
| 4. #22577636 | C2 | semidirect |
| 5. #22577441 | C2 | semidirect |
| 6. #22577408 | C2 | semidirect |
| 7. C22×D8×C137 | C2 | semidirect |
| 11. C2×#14555493 | C22 | semidirect |
| 12. C2×C8×D137 | C22 | semidirect |
| 15. #17984059 | C22 | semidirect |
| 18. #17984022 | C22 | semidirect |
| 19. #17984020 | C22 | semidirect |
| 20. #17984009 | C22 | semidirect |
| 49. C2×C8×C137 | D4 | semidirect |
| 93. C137 | #3058 | semidirect |
| 95. C22×D8 | D137 | semidirect |
| 139. C2×C8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984094 | 2 |
| #22577970 | 2 |
| #22577653 | 2 |
| #22577636 | 2 |
| #22577441 | 2 |
| #22577408 | 2 |
| C22×D8×C137 | 2 |
| #3058 | 137 |