Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
418 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581689 | C2 | semidirect |
| 2. #22581623 | C2 | semidirect |
| 3. #22581341 | C2 | semidirect |
| 4. #22581166 | C2 | semidirect |
| 5. #22581150 | C2 | semidirect |
| 6. #22581146 | C2 | semidirect |
| 7. #22581145 | C2 | semidirect |
| 8. #22581083 | C2 | semidirect |
| 9. #22581065 | C2 | semidirect |
| 10. C4×#14555774 | C2 | semidirect |
| 11. #493×C139 | C2 | semidirect |
| 108. C8×C139 | #41 | semidirect |
| 134. C139 | #3399 | semidirect |
| 139. #493 | D139 | semidirect |
| 243. C8 | #14555784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581689 | 2 |
| #22581623 | 2 |
| #22581341 | 2 |
| #22581166 | 2 |
| #22581150 | 2 |
| #22581146 | 2 |
| #22581145 | 2 |
| #22581083 | 2 |
| #22581065 | 2 |
| C4×#14555774 | 2 |
| #493×C139 | 2 |
| #3399 | 139 |