Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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. #22558423 | C2 | direct (N × H) |
| 3. C2×C67⋊C64 | C2 | semidirect |
| 4. C2×Q64×C67 | C2 | semidirect |
| 8. C67⋊C64 | C22 | semidirect |
| 11. Q64×C67 | C22 | semidirect |
| 47. C2×C67 | SD128 | semidirect |
| 50. C2×Q64 | D67 | semidirect |
| 54. C67 | C2×SD128 | semidirect |
| 58. Q64 | C2×D67 | semidirect |
| 97. C2 | #22558423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D2144 | 2 |
| #22558423 | 2 |
| C2×C67⋊C64 | 2 |
| C2×Q64×C67 | 2 |
| C2×SD128 | 67 |