Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #22581261 | C2 | semidirect |
| 5. #22581164 | C2 | semidirect |
| 7. #22581061 | C2 | semidirect |
| 8. C4×Dic556 | C2 | semidirect |
| 95. C139 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581565 | 2 |
| #22581430 | 2 |
| #22581295 | 2 |
| #22581261 | 2 |
| #22581164 | 2 |
| #22581111 | 2 |
| #22581061 | 2 |
| C4×Dic556 | 2 |
| #433×C139 | 2 |
| #3127 | 139 |