Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14555499 | C2 | semidirect |
| 2. #22577974 | C2 | semidirect |
| 4. #22577649 | C2 | semidirect |
| 5. #22577632 | C2 | semidirect |
| 6. #22577441 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577409 | C2 | semidirect |
| 9. C2×#131×C137 | C2 | semidirect |
| 20. #17984067 | C22 | semidirect |
| 25. #17984022 | C22 | semidirect |
| 26. #17984020 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 32. C2×M16×C137 | C22 | semidirect |
| 34. C22×C8×C137 | C22 | semidirect |
| 67. C2×C8×C137 | D4 | semidirect |
| 120. C137 | #3057 | semidirect |
| 123. C2×#131 | D137 | semidirect |
| 139. C2×M16 | C2×D137 | semidirect |
| 141. C22×C8 | C2×D137 | semidirect |
| 179. C2×C8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555499 | 2 |
| #22577974 | 2 |
| #22577967 | 2 |
| #22577649 | 2 |
| #22577632 | 2 |
| #22577441 | 2 |
| #22577413 | 2 |
| #22577409 | 2 |
| C2×#131×C137 | 2 |
| #3057 | 137 |