Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #22581058 | C2 | semidirect |
| 4. C4×#14555775 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 98. C139 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555775 | 2 |
| #22581430 | 2 |
| #22581058 | 2 |
| C4×#14555775 | 2 |
| #22580989 | 2 |
| #22580962 | 2 |
| #22580961 | 2 |
| #22580909 | 2 |
| #519×C139 | 2 |
| #2950 | 139 |