Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#17984765 | C2 | semidirect |
| 5. C2×#17984760 | C2 | semidirect |
| 6. #22580717 | C2 | semidirect |
| 7. #343×C139 | C2 | semidirect |
| 11. #17984875 | C4 | semidirect |
| 116. C139 | #1908 | semidirect |
| 123. #343 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984875 | 2 |
| C2×#17984850 | 2 |
| #22580952 | 2 |
| C2×#17984765 | 2 |
| C2×#17984760 | 2 |
| #22580717 | 2 |
| #343×C139 | 2 |
| #1908 | 139 |