Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 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. #22581508 | C2 | semidirect |
| 3. #22581290 | C2 | semidirect |
| 4. #22581230 | C2 | semidirect |
| 5. #22581159 | C2 | semidirect |
| 6. #22581158 | C2 | semidirect |
| 8. #22581052 | C2 | semidirect |
| 9. #22581050 | C2 | semidirect |
| 10. #22581009 | C2 | semidirect |
| 11. #474×C139 | C2 | semidirect |
| 16. #17984842 | C22 | semidirect |
| 21. #17984807 | C22 | semidirect |
| 31. #17984775 | C22 | semidirect |
| 32. C4⋊(C139⋊C8) | C22 | semidirect |
| 33. #17984767 | C22 | semidirect |
| 34. #17984765 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 38. C4⋊Q8×C139 | C22 | semidirect |
| 40. #107×C139 | C22 | semidirect |
| 41. C4⋊C8×C139 | C22 | semidirect |
| 146. C139 | #3110 | semidirect |
| 152. #474 | D139 | semidirect |
| 164. C4⋊Q8 | C2×D139 | semidirect |
| 181. #107 | C2×D139 | semidirect |
| 183. C4⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4×D4×D139 | 2 |
| #22581290 | 2 |
| #22581230 | 2 |
| #22581159 | 2 |
| #22581158 | 2 |
| #22581105 | 2 |
| #22581052 | 2 |
| #22581050 | 2 |
| #22581009 | 2 |
| #474×C139 | 2 |
| #3110 | 139 |