Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581263 | C2 | semidirect |
| 4. #22581259 | C2 | semidirect |
| 5. #22581247 | C2 | semidirect |
| 6. #22581237 | C2 | semidirect |
| 44. C2×Dic278 | Q8 | semidirect |
| 116. C139 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581584 | 2 |
| #22581430 | 2 |
| #22581263 | 2 |
| #22581259 | 2 |
| #22581247 | 2 |
| #22581237 | 2 |
| #22580989 | 2 |
| #22580981 | 2 |
| #22580963 | 2 |
| C2×#17984765 | 2 |
| #428×C139 | 2 |
| #3082 | 139 |