Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22581430 | C2 | semidirect |
| 4. C2×#17984760 | C2 | semidirect |
| 5. #22580710 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 10. #17984840 | C4 | semidirect |
| 11. #17984829 | C4 | semidirect |
| 109. C139 | #1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581524 | 2 |
| #22581430 | 2 |
| #22580970 | 2 |
| C2×#17984760 | 2 |
| #22580710 | 2 |
| #22580709 | 2 |
| #421×C139 | 2 |
| #1912 | 139 |