Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
612 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×C4×Dic274 | C2 | semidirect |
| 4. #22577309 | C2 | semidirect |
| 6. #22577295 | C2 | semidirect |
| 7. #22577277 | C2 | semidirect |
| 8. #22577273 | C2 | semidirect |
| 9. #376×C137 | C2 | semidirect |
| 13. #17984076 | C4 | semidirect |
| 33. C2×Dic274 | C2×C4 | semidirect |
| 48. #14555487 | C2×C4 | semidirect |
| 56. C42×C137 | C2×C4 | semidirect |
| 111. C137 | #2326 | semidirect |
| 121. #376 | D137 | semidirect |
| 168. C42 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984076 | 2 |
| C2×C4×Dic274 | 2 |
| C2×C4×D548 | 2 |
| #22577309 | 2 |
| #22577305 | 2 |
| #22577295 | 2 |
| #22577277 | 2 |
| #22577273 | 2 |
| #376×C137 | 2 |
| #2326 | 137 |