Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22581527 | C2 | semidirect |
| 3. #22581142 | C2 | semidirect |
| 4. #22580927 | C2 | semidirect |
| 5. #22580926 | C2 | semidirect |
| 6. #536×C139 | C2 | semidirect |
| 17. #17984825 | C22 | semidirect |
| 19. #17984801 | C22 | semidirect |
| 20. #17984757 | C22 | semidirect |
| 21. #17984756 | C22 | semidirect |
| 23. C22×Q8×C139 | C22 | semidirect |
| 26. #123×C139 | C22 | semidirect |
| 28. #117×C139 | C22 | semidirect |
| 128. C139 | #3028 | semidirect |
| 132. #536 | D139 | semidirect |
| 145. C22×Q8 | C2×D139 | semidirect |
| 151. #123 | C2×D139 | semidirect |
| 155. #117 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581789 | 2 |
| #22581527 | 2 |
| #22581142 | 2 |
| #22580927 | 2 |
| #22580926 | 2 |
| #536×C139 | 2 |
| #3028 | 139 |