Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. #22581768 | C2 | semidirect |
| 2. #22581767 | C2 | semidirect |
| 3. #22581331 | C2 | semidirect |
| 4. #22581228 | C2 | semidirect |
| 5. #22581226 | C2 | semidirect |
| 6. #22581225 | C2 | semidirect |
| 7. #22581136 | C2 | semidirect |
| 8. #22581134 | C2 | semidirect |
| 9. #22581070 | C2 | semidirect |
| 10. #22581068 | C2 | semidirect |
| 11. #578×C139 | C2 | semidirect |
| 146. C139 | #3293 | semidirect |
| 150. #578 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581768 | 2 |
| #22581767 | 2 |
| #22581331 | 2 |
| #22581228 | 2 |
| #22581226 | 2 |
| #22581225 | 2 |
| #22581136 | 2 |
| #22581134 | 2 |
| #22581070 | 2 |
| #22581068 | 2 |
| #578×C139 | 2 |
| #3293 | 139 |