Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22580969 | C2 | semidirect |
| 3. #22580949 | C2 | semidirect |
| 4. #22580947 | C2 | semidirect |
| 5. #22580926 | C2 | semidirect |
| 6. #22580921 | C2 | semidirect |
| 7. #421×C139 | C2 | semidirect |
| 10. #17984889 | C4 | semidirect |
| 12. #17984888 | C4 | semidirect |
| 20. C22×C139⋊C8 | C22 | semidirect |
| 21. #17984801 | C22 | semidirect |
| 30. C2×M16×C139 | C22 | semidirect |
| 31. #117×C139 | C22 | semidirect |
| 166. C139 | #1794 | semidirect |
| 170. #421 | D139 | semidirect |
| 188. C2×M16 | C2×D139 | semidirect |
| 191. #117 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581789 | 2 |
| #22580969 | 2 |
| #22580949 | 2 |
| #22580947 | 2 |
| #22580926 | 2 |
| #22580921 | 2 |
| #421×C139 | 2 |
| #1794 | 139 |