Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic139 | C2 | semidirect |
| 3. #22581286 | C2 | semidirect |
| 5. #22581258 | C2 | semidirect |
| 6. #22581177 | C2 | semidirect |
| 8. #22581060 | C2 | semidirect |
| 9. #22581056 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 11. #451×C139 | C2 | semidirect |
| 131. C139 | #3117 | semidirect |
| 139. #451 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581489 | 2 |
| C2×Q8×Dic139 | 2 |
| #22581286 | 2 |
| #22581272 | 2 |
| #22581258 | 2 |
| #22581177 | 2 |
| #22581092 | 2 |
| #22581060 | 2 |
| #22581056 | 2 |
| #22581007 | 2 |
| #451×C139 | 2 |
| #3117 | 139 |