Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22570585 | C2 | semidirect |
| 3. #22558922 | C2 | semidirect |
| 4. #22558807 | C2 | semidirect |
| 5. #22558721 | C2 | semidirect |
| 6. #22558101 | C2 | semidirect |
| 7. C67×#3215 | C2 | semidirect |
| 49. #14523954 | D4 | semidirect |
| 57. C4⋊Q8×C67 | D4 | semidirect |
| 58. C4⋊Q8×C67 | D4 | semidirect |
| 72. C4⋊C8×C67 | D4 | semidirect |
| 201. #3215 | D67 | semidirect |
| 208. C67 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D67 | semidirect |
| 242. C4⋊Q8 | C22⋊D67 | semidirect |
| 265. C4⋊C8 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570585 | 2 |
| #22566317 | 2 |
| #22558922 | 2 |
| #22558807 | 2 |
| #22558721 | 2 |
| #22558101 | 2 |
| C67×#3215 | 2 |
| #10096 | 67 |