Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 322 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. #22581260 | C2 | semidirect |
| 3. #22581257 | C2 | semidirect |
| 6. #22581163 | C2 | semidirect |
| 7. #22581160 | C2 | semidirect |
| 94. C139 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581565 | 2 |
| #22581260 | 2 |
| #22581257 | 2 |
| #22581209 | 2 |
| #22581192 | 2 |
| #22581163 | 2 |
| #22581160 | 2 |
| #22580980 | 2 |
| #541×C139 | 2 |
| #3261 | 139 |