Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22580777 | C2 | semidirect |
| 3. #22580768 | C2 | semidirect |
| 51. C139 | #2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581211 | 2 |
| #22580777 | 2 |
| #22580768 | 2 |
| #22580735 | 2 |
| #430×C139 | 2 |
| #2239 | 139 |