Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #22558368 | C2 | direct (N × H) |
| 7. C2×#14524043 | C4 | semidirect |
| 10. #16863791 | C4 | semidirect |
| 13. C2×#14523954 | C4 | semidirect |
| 33. #14524043 | C2×C4 | semidirect |
| 38. #14523954 | C2×C4 | semidirect |
| 151. C2×C67 | #1407 | semidirect |
| 157. C67 | C2×#1407 | semidirect |
| 303. C2 | #22558368 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863791 | 2 |
| C2×#16863193 | 2 |
| #22558368 | 2 |
| C2×#354×C67 | 2 |
| C2×#1407 | 67 |