Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
668 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22558210 | C2 | direct (N × H) |
| 5. C22×C4⋊Dic67 | C4 | semidirect |
| 10. #16863321 | C4 | semidirect |
| 13. C2×C67⋊#95 | C4 | semidirect |
| 26. C2×C4⋊Dic67 | C2×C4 | semidirect |
| 38. C67⋊#95 | C2×C4 | semidirect |
| 196. C2×C67 | #1344 | semidirect |
| 204. C67 | C2×#1344 | semidirect |
| 395. C2 | #22558210 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863321 | 2 |
| C2×#16863163 | 2 |
| #22558210 | 2 |
| C2×#323×C67 | 2 |
| C2×#1344 | 67 |