Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
526 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16863189 | C2 | semidirect |
| 2. #22558372 | C2 | direct (N × H) |
| 6. #16863189 | C22 | semidirect |
| 8. C2×#127×C67 | C4 | semidirect |
| 11. #493×C67 | C4 | semidirect |
| 13. C2×C4×C8×C67 | C4 | semidirect |
| 30. #127×C67 | C2×C4 | semidirect |
| 35. C4×C8×C67 | C2×C4 | semidirect |
| 122. C2×C67 | #1408 | semidirect |
| 127. C67 | C2×#1408 | semidirect |
| 129. C2×#127 | Dic67 | semidirect |
| 132. #493 | Dic67 | semidirect |
| 135. C2×C4×C8 | Dic67 | semidirect |
| 151. #127 | C2×Dic67 | semidirect |
| 159. C4×C8 | C2×Dic67 | semidirect |
| 245. C2 | #22558372 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863189 | 2 |
| #22558372 | 2 |
| C2×#493×C67 | 2 |
| C2×#1408 | 67 |