Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581267 | C2 | semidirect |
| 4. #22581264 | C2 | semidirect |
| 5. #22581246 | C2 | semidirect |
| 6. #22581151 | C2 | semidirect |
| 7. #22581092 | C2 | semidirect |
| 8. #22581056 | C2 | semidirect |
| 9. #22581054 | C2 | semidirect |
| 10. #22581007 | C2 | semidirect |
| 11. #448×C139 | C2 | semidirect |
| 104. Q8×C139 | #41 | semidirect |
| 140. C139 | #3112 | semidirect |
| 149. #448 | D139 | semidirect |
| 229. Q8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581498 | 2 |
| C2×Q8×Dic139 | 2 |
| #22581267 | 2 |
| #22581264 | 2 |
| #22581246 | 2 |
| #22581151 | 2 |
| #22581092 | 2 |
| #22581056 | 2 |
| #22581054 | 2 |
| #22581007 | 2 |
| #448×C139 | 2 |
| #3112 | 139 |