Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 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. #22580927 | C2 | semidirect |
| 4. #22580714 | C2 | semidirect |
| 5. #568×C139 | C2 | semidirect |
| 7. #17984840 | C4 | semidirect |
| 8. #17984838 | C4 | semidirect |
| 9. #17984831 | C4 | semidirect |
| 10. #17984829 | C4 | semidirect |
| 47. M16×C139 | D4 | semidirect |
| 95. C139 | #1884 | semidirect |
| 97. #568 | D139 | semidirect |
| 134. M16 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581499 | 2 |
| #22580969 | 2 |
| #22580927 | 2 |
| #22580714 | 2 |
| #568×C139 | 2 |
| #1884 | 139 |