Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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. #22562126 | C2 | semidirect |
| 3. #22561328 | C2 | semidirect |
| 4. #22558225 | C2 | semidirect |
| 5. #22558224 | C2 | semidirect |
| 6. #22558134 | C2 | semidirect |
| 7. C67×#2185 | C2 | semidirect |
| 20. C22⋊(C67⋊C16) | C22 | semidirect |
| 21. #16863161 | C22 | semidirect |
| 22. C22×Q16×C67 | C22 | semidirect |
| 26. C22⋊C16×C67 | C22 | semidirect |
| 187. #2185 | D67 | semidirect |
| 192. C67 | #12111 | semidirect |
| 194. C22×Q16 | C2×D67 | semidirect |
| 210. C22⋊C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571069 | 2 |
| #22562126 | 2 |
| #22561328 | 2 |
| #22558225 | 2 |
| #22558224 | 2 |
| #22558134 | 2 |
| C67×#2185 | 2 |
| #12111 | 67 |