Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22561982 | C2 | semidirect |
| 5. #22560999 | C2 | semidirect |
| 6. #22558324 | C2 | semidirect |
| 7. C67×#1378 | C2 | semidirect |
| 19. #16863210 | C4 | semidirect |
| 40. #14523979 | C2×C4 | semidirect |
| 51. M32×C67 | C2×C4 | semidirect |
| 144. #1378 | D67 | semidirect |
| 145. C67 | #12953 | semidirect |
| 181. M32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569062 | 2 |
| #22561982 | 2 |
| C2×#16863210 | 2 |
| #22560999 | 2 |
| #22558324 | 2 |
| C67×#1378 | 2 |
| #12953 | 67 |