Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 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. C2×#17984833 | C2 | semidirect |
| 3. #22581263 | C2 | semidirect |
| 4. #22581259 | C2 | semidirect |
| 5. #22581256 | C2 | semidirect |
| 6. #22581252 | C2 | semidirect |
| 7. #22580996 | C2 | semidirect |
| 8. #22580976 | C2 | semidirect |
| 11. #428×C139 | C2 | semidirect |
| 135. C139 | #3080 | semidirect |
| 144. #428 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984833 | 2 |
| #22581421 | 2 |
| #22581263 | 2 |
| #22581259 | 2 |
| #22581256 | 2 |
| #22581252 | 2 |
| #22580996 | 2 |
| #22580976 | 2 |
| #22580955 | 2 |
| #22580952 | 2 |
| #428×C139 | 2 |
| #3080 | 139 |