Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22562466 | C2 | semidirect |
| 2. D4×C67⋊C16 | C2 | semidirect |
| 4. #22558282 | C2 | semidirect |
| 5. #22558258 | C2 | semidirect |
| 6. #22558254 | C2 | semidirect |
| 7. C67×#1669 | C2 | semidirect |
| 56. C67⋊C16 | D8 | semidirect |
| 79. D4×C67 | SD32 | semidirect |
| 120. #1669 | D67 | semidirect |
| 125. C67 | #12432 | semidirect |
| 202. D4 | #14523986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562466 | 2 |
| D4×C67⋊C16 | 2 |
| #22559564 | 2 |
| #22558282 | 2 |
| #22558258 | 2 |
| #22558254 | 2 |
| C67×#1669 | 2 |
| #12432 | 67 |