Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
190 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#16863236 | C2 | semidirect |
| 5. #22558410 | C2 | semidirect |
| 6. #22558391 | C2 | semidirect |
| 7. C67×#1416 | C2 | semidirect |
| 98. #1416 | D67 | semidirect |
| 99. C67 | #13698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863236 | 2 |
| C2×#16863229 | 2 |
| #22562301 | 2 |
| #22562297 | 2 |
| #22558410 | 2 |
| #22558391 | 2 |
| C67×#1416 | 2 |
| #13698 | 67 |