Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22580963 | C2 | semidirect |
| 4. C2×#17984760 | C2 | semidirect |
| 5. #22580725 | C2 | semidirect |
| 6. C139⋊#338 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 12. C2×#14555773 | C4 | semidirect |
| 107. C139 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| #22580970 | 2 |
| #22580963 | 2 |
| C2×#17984760 | 2 |
| #22580725 | 2 |
| C139⋊#338 | 2 |
| #568×C139 | 2 |
| #1902 | 139 |