Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
276 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 276 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. #22561991 | C2 | semidirect |
| 5. #22558311 | C2 | semidirect |
| 6. #22558306 | C2 | semidirect |
| 7. C67×#1389 | C2 | semidirect |
| 140. #1389 | D67 | semidirect |
| 143. C67 | #13500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561991 | 2 |
| C2×#16863181 | 2 |
| #22560264 | 2 |
| #22560252 | 2 |
| #22558311 | 2 |
| #22558306 | 2 |
| C67×#1389 | 2 |
| #13500 | 67 |