Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 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. #22561154 | C2 | semidirect |
| 5. #22558073 | C2 | semidirect |
| 6. #22558066 | C2 | semidirect |
| 7. C67×#1515 | C2 | semidirect |
| 9. #16863788 | C4 | semidirect |
| 10. #16863758 | C4 | semidirect |
| 56. #14523954 | C2×C4 | semidirect |
| 61. C4⋊Q8×C67 | C2×C4 | semidirect |
| 62. C4⋊Q8×C67 | C2×C4 | semidirect |
| 209. #1515 | D67 | semidirect |
| 212. C67 | #9379 | semidirect |
| 242. C4⋊Q8 | C4×D67 | semidirect |
| 243. C4⋊Q8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571208 | 2 |
| #22563019 | 2 |
| #22561154 | 2 |
| #22558808 | 2 |
| #22558073 | 2 |
| #22558066 | 2 |
| C67×#1515 | 2 |
| #9379 | 67 |