Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#17984849 | C2 | semidirect |
| 2. #22581075 | C2 | semidirect |
| 3. #22581070 | C2 | semidirect |
| 4. #22581002 | C2 | semidirect |
| 5. #22580970 | C2 | semidirect |
| 6. #22580911 | C2 | semidirect |
| 10. #17984849 | C22 | semidirect |
| 11. #17984849 | C22 | semidirect |
| 17. #17984778 | C22 | semidirect |
| 18. #17984769 | C22 | semidirect |
| 19. #17984752 | C22 | semidirect |
| 20. C8×Dic139 | C22 | semidirect |
| 22. #137×C139 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C139 | C4 | semidirect |
| 89. C139 | #2955 | semidirect |
| 99. #137 | Dic139 | semidirect |
| 100. AGL(1,ℤ/8) | Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984849 | 2 |
| #22581075 | 2 |
| #22581070 | 2 |
| #22581002 | 2 |
| #22580970 | 2 |
| #22580911 | 2 |
| #575×C139 | 2 |
| #2955 | 139 |