Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
262 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22581001 | C2 | semidirect |
| 3. #22580976 | C2 | semidirect |
| 5. #22580723 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 17. #17984769 | C4 | semidirect |
| 18. #17984769 | C4 | semidirect |
| 97. C139 | #1861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581720 | 2 |
| #22581001 | 2 |
| #22580976 | 2 |
| C2×#17984769 | 2 |
| #22580723 | 2 |
| #22580712 | 2 |
| #421×C139 | 2 |
| #1861 | 139 |