Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
| 3. #22578267 | C2 | semidirect |
| 4. Q8⋊#11764047 | C2 | semidirect |
| 6. #22578244 | C2 | semidirect |
| 31. #14555497 | C8 | semidirect |
| 54. #11764040 | C2×C8 | semidirect |
| 56. Q8×C137 | C2×C8 | semidirect |
| 77. C137 | SD16⋊C8 | semidirect |
| 121. 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 |
| #22578267 | 2 |
| Q8⋊#11764047 | 2 |
| #22578251 | 2 |
| #22578244 | 2 |
| #22577488 | 2 |
| SD16⋊C8 | 137 |