Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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×#17984833 | C2 | semidirect |
| 3. #22581320 | C2 | semidirect |
| 4. #22581316 | C2 | semidirect |
| 5. #22581309 | C2 | semidirect |
| 6. #22581306 | C2 | semidirect |
| 7. #22580955 | C2 | semidirect |
| 8. #22580954 | C2 | semidirect |
| 9. #22580952 | C2 | semidirect |
| 10. M16×Dic139 | C2 | semidirect |
| 11. #417×C139 | C2 | semidirect |
| 146. C139 | #3142 | semidirect |
| 157. #417 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581499 | 2 |
| C2×#17984833 | 2 |
| #22581320 | 2 |
| #22581316 | 2 |
| #22581309 | 2 |
| #22581306 | 2 |
| #22580955 | 2 |
| #22580954 | 2 |
| #22580952 | 2 |
| M16×Dic139 | 2 |
| #417×C139 | 2 |
| #3142 | 139 |