Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 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 |
|---|---|---|
| 1. #22581689 | C2 | direct (N × H) |
| 2. C2×#17984829 | C2 | semidirect |
| 3. C2×#17984823 | C2 | semidirect |
| 4. C2×C4×Dic278 | C2 | semidirect |
| 5. C2×D4×Dic139 | C2 | semidirect |
| 9. #17984829 | C22 | semidirect |
| 10. #17984823 | C22 | semidirect |
| 11. C4×Dic278 | C22 | semidirect |
| 12. D4×Dic139 | C22 | semidirect |
| 68. C2×C139 | #559 | semidirect |
| 71. C139 | C2×#559 | semidirect |
| 140. C2 | #22581689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581689 | 2 |
| C2×#17984829 | 2 |
| C2×#17984823 | 2 |
| C2×C4×Dic278 | 2 |
| C2×D4×Dic139 | 2 |
| C2×#127×C139 | 2 |
| C2×#559 | 139 |