Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 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. #22580962 | C2 | semidirect |
| 5. #22580723 | C2 | semidirect |
| 6. #22580709 | C2 | semidirect |
| 7. #519×C139 | C2 | semidirect |
| 11. C2×#14555775 | C4 | semidirect |
| 12. C2×#14555772 | C4 | semidirect |
| 109. C139 | #1905 | semidirect |
| 112. #519 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984873 | 2 |
| #22580971 | 2 |
| #22580962 | 2 |
| #22580926 | 2 |
| #22580723 | 2 |
| #22580709 | 2 |
| #519×C139 | 2 |
| #1905 | 139 |