Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 342 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. #22581238 | C2 | semidirect |
| 3. #22581235 | C2 | semidirect |
| 5. #22581163 | C2 | semidirect |
| 6. #22581160 | C2 | semidirect |
| 104. C139 | #3255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581238 | 2 |
| #22581235 | 2 |
| #22581209 | 2 |
| #22581163 | 2 |
| #22581160 | 2 |
| #22580977 | 2 |
| #533×C139 | 2 |
| #3255 | 139 |