Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
222 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22580981 | C2 | semidirect |
| 5. C2×#17984752 | C2 | semidirect |
| 6. #22580714 | C2 | semidirect |
| 7. #341×C139 | C2 | semidirect |
| 14. #17984767 | C4 | semidirect |
| 15. #17984764 | C4 | semidirect |
| 90. C139 | #1938 | semidirect |
| 97. #341 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580981 | 2 |
| C2×#17984768 | 2 |
| #22580950 | 2 |
| #22580921 | 2 |
| C2×#17984752 | 2 |
| #22580714 | 2 |
| #341×C139 | 2 |
| #1938 | 139 |