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 |
|---|---|---|
| 2. #22580969 | C2 | semidirect |
| 3. #22580949 | C2 | semidirect |
| 4. #22580921 | C2 | semidirect |
| 5. #22580724 | C2 | semidirect |
| 6. #22580717 | C2 | semidirect |
| 7. #568×C139 | C2 | semidirect |
| 10. #17984872 | C4 | semidirect |
| 12. #17984867 | C4 | semidirect |
| 118. C139 | #1881 | semidirect |
| 121. #568 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581751 | 2 |
| #22580969 | 2 |
| #22580949 | 2 |
| #22580921 | 2 |
| #22580724 | 2 |
| #22580717 | 2 |
| #568×C139 | 2 |
| #1881 | 139 |