Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22562432 | C2 | semidirect |
| 2. #22562356 | C2 | semidirect |
| 3. #22559608 | C2 | semidirect |
| 4. #22558255 | C2 | semidirect |
| 5. #22558170 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 8. #16863801 | C22 | semidirect |
| 11. C4⋊(C67⋊C16) | C22 | semidirect |
| 14. C4×C67⋊C16 | C22 | semidirect |
| 15. #16863149 | C22 | semidirect |
| 157. C67 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562432 | 2 |
| #22562356 | 2 |
| #22559608 | 2 |
| #22558255 | 2 |
| #22558170 | 2 |
| D4⋊(C67⋊C16) | 2 |
| D4×D8×C67 | 2 |
| #12372 | 67 |