Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581501 | C2 | semidirect |
| 2. #22581488 | C2 | semidirect |
| 3. #22581363 | C2 | semidirect |
| 4. #22581340 | C2 | semidirect |
| 5. #22581313 | C2 | semidirect |
| 6. #22581205 | C2 | semidirect |
| 7. #22581198 | C2 | semidirect |
| 8. #22581044 | C2 | semidirect |
| 9. #22581033 | C2 | semidirect |
| 10. #22580905 | C2 | semidirect |
| 11. #490×C139 | C2 | semidirect |
| 99. C139⋊C8 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 143. #490 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581501 | 2 |
| #22581488 | 2 |
| #22581363 | 2 |
| #22581340 | 2 |
| #22581313 | 2 |
| #22581205 | 2 |
| #22581198 | 2 |
| #22581044 | 2 |
| #22581033 | 2 |
| #22580905 | 2 |
| #490×C139 | 2 |
| #3171 | 139 |