Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#16863173 | C2 | semidirect |
| 5. #22560096 | C2 | semidirect |
| 6. #22558316 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 12. #16863507 | C4 | semidirect |
| 17. #16863208 | C4 | semidirect |
| 18. #16863198 | C4 | semidirect |
| 39. #14523983 | C2×C4 | semidirect |
| 41. #14523977 | C2×C4 | semidirect |
| 53. C2×C16×C67 | C2×C4 | semidirect |
| 55. #108×C67 | C2×C4 | semidirect |
| 152. #1383 | D67 | semidirect |
| 153. C67 | #12647 | semidirect |
| 192. C2×C16 | C4×D67 | semidirect |
| 194. #108 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863507 | 2 |
| C2×#16863208 | 2 |
| #22561926 | 2 |
| C2×#16863173 | 2 |
| #22560096 | 2 |
| #22558316 | 2 |
| C67×#1383 | 2 |
| #12647 | 67 |