Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581296 | C2 | semidirect |
| 4. #22581268 | C2 | semidirect |
| 5. #22581245 | C2 | semidirect |
| 6. #22581240 | C2 | semidirect |
| 7. #22581200 | C2 | semidirect |
| 8. C4×#14555774 | C2 | semidirect |
| 9. #22581032 | C2 | semidirect |
| 10. #22580994 | C2 | semidirect |
| 11. #500×C139 | C2 | semidirect |
| 121. C139 | #3357 | semidirect |
| 125. #500 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581669 | 2 |
| #22581664 | 2 |
| #22581296 | 2 |
| #22581268 | 2 |
| #22581245 | 2 |
| #22581240 | 2 |
| #22581200 | 2 |
| C4×#14555774 | 2 |
| #22581032 | 2 |
| #22580994 | 2 |
| #500×C139 | 2 |
| #3357 | 139 |