Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #22581664 | C2 | semidirect |
| 3. #22581356 | C2 | semidirect |
| 4. #22581297 | C2 | semidirect |
| 5. #22581265 | C2 | semidirect |
| 6. #22581249 | C2 | semidirect |
| 7. #22581198 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. #22581030 | C2 | semidirect |
| 10. #22580992 | C2 | semidirect |
| 11. #476×C139 | C2 | semidirect |
| 121. C139 | #3357 | semidirect |
| 129. #476 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581664 | 2 |
| #22581356 | 2 |
| #22581297 | 2 |
| #22581265 | 2 |
| #22581249 | 2 |
| #22581198 | 2 |
| C4×#14555773 | 2 |
| #22581030 | 2 |
| #22580992 | 2 |
| #476×C139 | 2 |
| #3357 | 139 |