Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic278 | C2 | semidirect |
| 2. #22581286 | C2 | semidirect |
| 4. #22581257 | C2 | semidirect |
| 5. #22581172 | C2 | semidirect |
| 6. #22581108 | C2 | semidirect |
| 8. #22581058 | C2 | semidirect |
| 9. #22581053 | C2 | semidirect |
| 10. #22581010 | C2 | semidirect |
| 131. C139 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic278 | 2 |
| #22581286 | 2 |
| #22581269 | 2 |
| #22581257 | 2 |
| #22581172 | 2 |
| #22581108 | 2 |
| #22581091 | 2 |
| #22581058 | 2 |
| #22581053 | 2 |
| #22581010 | 2 |
| #529×C139 | 2 |
| #3117 | 139 |