Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
| 5. #22558322 | C2 | semidirect |
| 6. #22558303 | C2 | semidirect |
| 7. C67×#1382 | C2 | semidirect |
| 136. #1382 | D67 | semidirect |
| 138. C67 | #13503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561981 | 2 |
| C2×#16863179 | 2 |
| #22560260 | 2 |
| #22560256 | 2 |
| #22558322 | 2 |
| #22558303 | 2 |
| C67×#1382 | 2 |
| #13503 | 67 |