Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #22581688 | C2 | semidirect |
| 2. #22581660 | C2 | semidirect |
| 3. #22581309 | C2 | semidirect |
| 4. #22581300 | C2 | semidirect |
| 5. #22581252 | C2 | semidirect |
| 6. #22581248 | C2 | semidirect |
| 7. #22581170 | C2 | semidirect |
| 9. C8×Dic278 | C2 | semidirect |
| 10. #22581033 | C2 | semidirect |
| 11. C4×SD16×C139 | C2 | semidirect |
| 122. C139 | #3361 | semidirect |
| 133. C4×SD16 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581660 | 2 |
| #22581309 | 2 |
| #22581300 | 2 |
| #22581252 | 2 |
| #22581248 | 2 |
| #22581170 | 2 |
| #22581148 | 2 |
| C8×Dic278 | 2 |
| #22581033 | 2 |
| C4×SD16×C139 | 2 |
| #3361 | 139 |