Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22565434 | C2 | semidirect |
| 5. #22558087 | C2 | semidirect |
| 6. #22558055 | C2 | semidirect |
| 7. C67×#1289 | C2 | semidirect |
| 228. #1289 | D67 | semidirect |
| 230. C67 | #10376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22565434 | 2 |
| #22561044 | 2 |
| #22558776 | 2 |
| C2×#16863131 | 2 |
| #22558087 | 2 |
| #22558055 | 2 |
| C67×#1289 | 2 |
| #10376 | 67 |