Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22580911 | C2 | semidirect |
| 5. C2×#17984752 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 7. #341×C139 | C2 | semidirect |
| 10. #17984850 | C4 | semidirect |
| 16. #17984768 | C4 | semidirect |
| 17. #17984767 | C4 | semidirect |
| 18. #17984764 | C4 | semidirect |
| 98. C139 | #1765 | semidirect |
| 105. #341 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984850 | 2 |
| C2×#17984768 | 2 |
| #22580950 | 2 |
| #22580911 | 2 |
| C2×#17984752 | 2 |
| #22580714 | 2 |
| #341×C139 | 2 |
| #1765 | 139 |