Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. C2×#17984800 | C2 | semidirect |
| 3. #22581297 | C2 | semidirect |
| 4. #22581288 | C2 | semidirect |
| 5. #22581284 | C2 | semidirect |
| 6. #22581276 | C2 | semidirect |
| 7. #22581264 | C2 | semidirect |
| 8. #22580988 | C2 | semidirect |
| 9. #22580946 | C2 | semidirect |
| 10. C22⋊C8×D139 | C2 | semidirect |
| 11. #481×C139 | C2 | semidirect |
| 30. #17984775 | C22 | semidirect |
| 31. #17984775 | C22 | semidirect |
| 32. #17984774 | C22 | semidirect |
| 33. #17984767 | C22 | semidirect |
| 34. #17984765 | C22 | semidirect |
| 35. #17984763 | C22 | semidirect |
| 40. #106×C139 | C22 | semidirect |
| 41. #102×C139 | C22 | semidirect |
| 143. C139 | #3091 | semidirect |
| 151. #481 | D139 | semidirect |
| 179. #106 | C2×D139 | semidirect |
| 183. #102 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581463 | 2 |
| C2×#17984800 | 2 |
| #22581297 | 2 |
| #22581288 | 2 |
| #22581284 | 2 |
| #22581276 | 2 |
| #22581264 | 2 |
| #22580988 | 2 |
| #22580946 | 2 |
| C22⋊C8×D139 | 2 |
| #481×C139 | 2 |
| #3091 | 139 |