Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #22581720 | C2 | semidirect |
| 3. #22580935 | C2 | semidirect |
| 4. C2×#17984758 | C2 | semidirect |
| 5. #568×C139 | C2 | semidirect |
| 13. C2×#14555769 | C22 | semidirect |
| 14. #17984760 | C22 | semidirect |
| 15. #17984758 | C22 | semidirect |
| 18. C2×M16×C139 | C22 | semidirect |
| 76. C139 | #2888 | semidirect |
| 80. #568 | D139 | semidirect |
| 93. C2×M16 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984888 | 2 |
| #22581720 | 2 |
| #22580935 | 2 |
| C2×#17984758 | 2 |
| #568×C139 | 2 |
| #2888 | 139 |