Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 2. #22580970 | C2 | semidirect |
| 3. #22580959 | C2 | semidirect |
| 4. C2×#17984758 | C2 | semidirect |
| 5. #22580725 | C2 | semidirect |
| 6. C139⋊#338 | C2 | semidirect |
| 7. #568×C139 | C2 | semidirect |
| 11. C2×#14555772 | C4 | semidirect |
| 12. C2×#14555770 | C4 | semidirect |
| 112. C139 | #1903 | semidirect |
| 115. #568 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984867 | 2 |
| #22580970 | 2 |
| #22580959 | 2 |
| C2×#17984758 | 2 |
| #22580725 | 2 |
| C139⋊#338 | 2 |
| #568×C139 | 2 |
| #1903 | 139 |