Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
432 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 204 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. Q8×#11764047 | C2 | semidirect |
| 2. #22578431 | C2 | semidirect |
| 3. #22578421 | C2 | semidirect |
| 4. #22578404 | C2 | semidirect |
| 22. #14555511 | C8 | semidirect |
| 38. D548 | C2×C8 | semidirect |
| 45. C4×D137 | C2×C8 | semidirect |
| 46. Q8×C137 | C2×C8 | semidirect |
| 65. C137 | #2988 | semidirect |
| 102. Q8 | #14555518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764047 | 2 |
| #22578431 | 2 |
| #22578421 | 2 |
| #22578404 | 2 |
| C4×#14555511 | 2 |
| #2988 | 137 |