Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16863221 | C2 | semidirect |
| 4. #22560992 | C2 | semidirect |
| 5. #22558318 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 19. #16863203 | C4 | semidirect |
| 37. C2×C67⋊C16 | C2×C4 | semidirect |
| 39. #14523979 | C2×C4 | semidirect |
| 167. C67 | #12945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569085 | 2 |
| C2×#16863221 | 2 |
| C2×#16863203 | 2 |
| #22560992 | 2 |
| #22558318 | 2 |
| #22558299 | 2 |
| C67×#2139 | 2 |
| #12945 | 67 |