Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#16863218 | C2 | semidirect |
| 4. #22560962 | C2 | semidirect |
| 5. #22558316 | C2 | semidirect |
| 6. #22558289 | C2 | semidirect |
| 15. #16863197 | C4 | semidirect |
| 31. C2×C67⋊C16 | C2×C4 | semidirect |
| 34. #14523977 | C2×C4 | semidirect |
| 152. C67 | #12956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863218 | 2 |
| C2×#16863209 | 2 |
| #22561925 | 2 |
| #22560962 | 2 |
| #22558316 | 2 |
| #22558289 | 2 |
| C2×#442×C67 | 2 |
| #12956 | 67 |