Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22561981 | C2 | semidirect |
| 2. #22561974 | C2 | semidirect |
| 6. #22560987 | C2 | semidirect |
| 7. C67×#1386 | C2 | semidirect |
| 146. #1386 | D67 | semidirect |
| 147. C67 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561981 | 2 |
| #22561974 | 2 |
| C2×#16863205 | 2 |
| #22561938 | 2 |
| #22561105 | 2 |
| #22560987 | 2 |
| C67×#1386 | 2 |
| #13469 | 67 |