Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
484 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 109 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. #135×Dic67 | C2 | semidirect |
| 3. #22561946 | C2 | semidirect |
| 4. #22561095 | C2 | semidirect |
| 5. #22558323 | C2 | semidirect |
| 6. #22558290 | C2 | semidirect |
| 7. C67×#2143 | C2 | semidirect |
| 11. #16863836 | C4 | semidirect |
| 13. #16863831 | C4 | semidirect |
| 34. C2×Dic268 | C2×C4 | semidirect |
| 36. C2×D536 | C2×C4 | semidirect |
| 50. #14523983 | C2×C4 | semidirect |
| 195. #2143 | D67 | semidirect |
| 199. C67 | #13027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573343 | 2 |
| #135×Dic67 | 2 |
| #22561946 | 2 |
| #22561095 | 2 |
| #22558323 | 2 |
| #22558290 | 2 |
| C67×#2143 | 2 |
| #13027 | 67 |