Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. #22581507 | C2 | semidirect |
| 3. #22581249 | C2 | semidirect |
| 4. #22581248 | C2 | semidirect |
| 5. #22581231 | C2 | semidirect |
| 6. #22581198 | C2 | semidirect |
| 7. #22581196 | C2 | semidirect |
| 8. #22581156 | C2 | semidirect |
| 9. #22581150 | C2 | semidirect |
| 10. #22580975 | C2 | semidirect |
| 11. #460×C139 | C2 | semidirect |
| 137. C139 | #3254 | semidirect |
| 148. #460 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581507 | 2 |
| #22581501 | 2 |
| #22581249 | 2 |
| #22581248 | 2 |
| #22581231 | 2 |
| #22581198 | 2 |
| #22581196 | 2 |
| #22581156 | 2 |
| #22581150 | 2 |
| #22580975 | 2 |
| #460×C139 | 2 |
| #3254 | 139 |