Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22581678 | C2 | semidirect |
| 3. #22581306 | C2 | semidirect |
| 4. #22581251 | C2 | semidirect |
| 5. #22581235 | C2 | semidirect |
| 6. #22581174 | C2 | semidirect |
| 8. C8×Dic278 | C2 | semidirect |
| 9. C4×Dic556 | C2 | semidirect |
| 10. #22581044 | C2 | semidirect |
| 117. C139 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581689 | 2 |
| #22581678 | 2 |
| #22581306 | 2 |
| #22581251 | 2 |
| #22581235 | 2 |
| #22581174 | 2 |
| #22581150 | 2 |
| C8×Dic278 | 2 |
| C4×Dic556 | 2 |
| #22581044 | 2 |
| #486×C139 | 2 |
| #3365 | 139 |