Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
852 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22571016 | C2 | semidirect |
| 2. C2×#16863547 | C2 | semidirect |
| 4. #22558574 | C2 | semidirect |
| 5. #22558570 | C2 | semidirect |
| 6. #22558096 | C2 | semidirect |
| 7. C67×#1783 | C2 | semidirect |
| 235. #1783 | D67 | semidirect |
| 239. C67 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571016 | 2 |
| C2×#16863547 | 2 |
| C2×#16863530 | 2 |
| #22558574 | 2 |
| #22558570 | 2 |
| #22558096 | 2 |
| C67×#1783 | 2 |
| #9987 | 67 |