Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581504 | C2 | semidirect |
| 2. C4×D4×D139 | C2 | semidirect |
| 3. #22581273 | C2 | semidirect |
| 4. #22581240 | C2 | semidirect |
| 5. #22581149 | C2 | semidirect |
| 6. #22581148 | C2 | semidirect |
| 7. #22581088 | C2 | semidirect |
| 8. #22581064 | C2 | semidirect |
| 9. #22581062 | C2 | semidirect |
| 10. #22581009 | C2 | semidirect |
| 11. #476×C139 | C2 | semidirect |
| 17. #17984839 | C22 | semidirect |
| 25. #17984804 | C22 | semidirect |
| 31. #17984773 | C22 | semidirect |
| 32. C4⋊(C139⋊C8) | C22 | semidirect |
| 33. #17984764 | C22 | semidirect |
| 35. #17984762 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 38. C4⋊Q8×C139 | C22 | semidirect |
| 40. #106×C139 | C22 | semidirect |
| 41. C4⋊C8×C139 | C22 | semidirect |
| 96. D556 | #41 | semidirect |
| 115. D4×C139 | #41 | semidirect |
| 154. C139 | #3109 | semidirect |
| 160. #476 | D139 | semidirect |
| 172. C4⋊Q8 | C2×D139 | semidirect |
| 189. #106 | C2×D139 | semidirect |
| 191. C4⋊C8 | C2×D139 | semidirect |
| 256. D4 | #14555786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581504 | 2 |
| C4×D4×D139 | 2 |
| #22581273 | 2 |
| #22581240 | 2 |
| #22581149 | 2 |
| #22581148 | 2 |
| #22581088 | 2 |
| #22581064 | 2 |
| #22581062 | 2 |
| #22581009 | 2 |
| #476×C139 | 2 |
| #3109 | 139 |