Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22581581 | C2 | semidirect |
| 3. #22581254 | C2 | semidirect |
| 4. #22581254 | C2 | semidirect |
| 5. #22581244 | C2 | semidirect |
| 6. #22581234 | C2 | semidirect |
| 7. #22580995 | C2 | semidirect |
| 8. #22580991 | C2 | semidirect |
| 11. #424×C139 | C2 | semidirect |
| 13. #17984842 | C22 | semidirect |
| 15. #17984834 | C22 | semidirect |
| 26. #17984776 | C22 | semidirect |
| 27. #17984776 | C22 | semidirect |
| 28. #17984776 | C22 | semidirect |
| 29. #17984774 | C22 | semidirect |
| 30. #17984774 | C22 | semidirect |
| 31. #17984774 | C22 | semidirect |
| 39. C4⋊C8×C139 | C22 | semidirect |
| 40. C4⋊C8×C139 | C22 | semidirect |
| 45. C2×D556 | Q8 | semidirect |
| 124. C139 | #3081 | semidirect |
| 134. #424 | D139 | semidirect |
| 160. C4⋊C8 | C2×D139 | semidirect |
| 161. C4⋊C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581427 | 2 |
| #22581254 | 2 |
| #22581244 | 2 |
| #22581234 | 2 |
| #22580995 | 2 |
| #22580991 | 2 |
| #22580959 | 2 |
| C2×#17984764 | 2 |
| #424×C139 | 2 |
| #3081 | 139 |