Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
354 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #22581660 | C2 | semidirect |
| 3. #22581358 | C2 | semidirect |
| 4. #22581295 | C2 | semidirect |
| 5. #22581267 | C2 | semidirect |
| 6. #22581249 | C2 | semidirect |
| 7. #22581244 | C2 | semidirect |
| 8. #22581199 | C2 | semidirect |
| 9. C4×#14555774 | C2 | semidirect |
| 10. #22580995 | C2 | semidirect |
| 11. #436×C139 | C2 | semidirect |
| 121. C139 | #3357 | semidirect |
| 132. #436 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581668 | 2 |
| #22581660 | 2 |
| #22581358 | 2 |
| #22581295 | 2 |
| #22581267 | 2 |
| #22581249 | 2 |
| #22581244 | 2 |
| #22581199 | 2 |
| C4×#14555774 | 2 |
| #22580995 | 2 |
| #436×C139 | 2 |
| #3357 | 139 |