Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
448 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C22⋊C16×D67 | C2 | semidirect |
| 3. #22560246 | C2 | semidirect |
| 4. #22558225 | C2 | semidirect |
| 5. #22558224 | C2 | semidirect |
| 6. #22558223 | C2 | semidirect |
| 7. C67×#1349 | C2 | semidirect |
| 21. C22⋊(C67⋊C16) | C22 | semidirect |
| 23. #16863161 | C22 | semidirect |
| 25. C22⋊C16×C67 | C22 | semidirect |
| 26. #341×C67 | C22 | semidirect |
| 195. #1349 | D67 | semidirect |
| 196. C67 | #11891 | semidirect |
| 213. C22⋊C16 | C2×D67 | semidirect |
| 215. #341 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D67 | 2 |
| C22⋊C16×D67 | 2 |
| #22560246 | 2 |
| #22558225 | 2 |
| #22558224 | 2 |
| #22558223 | 2 |
| C67×#1349 | 2 |
| #11891 | 67 |