Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22578421 | C2 | semidirect |
| 2. #22578404 | C2 | semidirect |
| 3. Q8⋊#11764047 | C2 | semidirect |
| 4. #22578251 | C2 | semidirect |
| 27. #14555511 | C8 | semidirect |
| 57. D548 | C2×C8 | semidirect |
| 72. Q8×C137 | C2×C8 | semidirect |
| 101. C137 | #1477 | semidirect |
| 156. Q8 | #14555518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578421 | 2 |
| #22578404 | 2 |
| Q8⋊#11764047 | 2 |
| #22578251 | 2 |
| C4×#14555511 | 2 |
| #1477 | 137 |