Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
538 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22560286 | C2 | semidirect |
| 5. #22558118 | C2 | semidirect |
| 6. #22558062 | C2 | semidirect |
| 7. C67×#1826 | C2 | semidirect |
| 10. #16863714 | C4 | semidirect |
| 11. #16863709 | C4 | semidirect |
| 54. C22⋊(C67⋊C8) | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C67 | C2×C4 | semidirect |
| 68. C2×C4⋊C4×C67 | C2×C4 | semidirect |
| 234. #1826 | D67 | semidirect |
| 239. C67 | #9525 | semidirect |
| 279. C2×C4⋊C4 | C4×D67 | semidirect |
| 280. C2×C4⋊C4 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570149 | 2 |
| #22562974 | 2 |
| #22560286 | 2 |
| #22558739 | 2 |
| #22558118 | 2 |
| #22558062 | 2 |
| C67×#1826 | 2 |
| #9525 | 67 |