Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 1. C4⋊Q8×D139 | C2 | semidirect |
| 3. #22581248 | C2 | semidirect |
| 4. #22581244 | C2 | semidirect |
| 5. #22581240 | C2 | semidirect |
| 6. #22581236 | C2 | semidirect |
| 7. #22581232 | C2 | semidirect |
| 8. #22580994 | C2 | semidirect |
| 9. #22580975 | C2 | semidirect |
| 11. #477×C139 | C2 | semidirect |
| 44. #14555786 | Q8 | semidirect |
| 88. D556 | C2×Q8 | semidirect |
| 105. Q8×C139 | C2×Q8 | semidirect |
| 137. C139 | #3079 | semidirect |
| 142. #477 | D139 | semidirect |
| 226. Q8 | Q8×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D139 | 2 |
| C4×#14555786 | 2 |
| #22581248 | 2 |
| #22581244 | 2 |
| #22581240 | 2 |
| #22581236 | 2 |
| #22581232 | 2 |
| #22580994 | 2 |
| #22580975 | 2 |
| #22580953 | 2 |
| #477×C139 | 2 |
| #3079 | 139 |