Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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×#17984053 | C2 | semidirect |
| 4. #22577308 | C2 | semidirect |
| 6. #22577293 | C2 | semidirect |
| 7. #22577274 | C2 | semidirect |
| 8. #22577249 | C2 | semidirect |
| 9. #384×C137 | C2 | semidirect |
| 13. #17984076 | C4 | semidirect |
| 33. C2×Dic274 | C2×C4 | semidirect |
| 46. #14555487 | C2×C4 | semidirect |
| 57. C42×C137 | C2×C4 | semidirect |
| 111. C137 | #2326 | semidirect |
| 120. #384 | D137 | semidirect |
| 169. 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×#17984053 | 2 |
| C2×#17984050 | 2 |
| #22577308 | 2 |
| #22577304 | 2 |
| #22577293 | 2 |
| #22577274 | 2 |
| #22577249 | 2 |
| #384×C137 | 2 |
| #2326 | 137 |