Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 3. #22578253 | C2 | semidirect |
| 4. Q8⋊#11764047 | C2 | semidirect |
| 30. Q8×D137 | C8 | semidirect |
| 57. Dic274 | C2×C8 | semidirect |
| 71. Q8×C137 | C2×C8 | semidirect |
| 96. D137 | Q8⋊C8 | semidirect |
| 97. C137 | C2×Q8⋊C8 | semidirect |
| 155. Q8 | #14555518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| C4×#14555518 | 2 |
| #22578253 | 2 |
| Q8⋊#11764047 | 2 |
| C4×Q8×D137 | 2 |
| C2×Q8⋊C8 | 137 |