Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
544 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22571355 | C2 | semidirect |
| 4. #22561053 | C2 | semidirect |
| 6. #22558665 | C2 | semidirect |
| 7. C67×#1278 | C2 | semidirect |
| 180. #1278 | D67 | semidirect |
| 181. C67 | #10151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571355 | 2 |
| #22570584 | 2 |
| C2×#16863743 | 2 |
| #22561053 | 2 |
| #22558876 | 2 |
| #22558665 | 2 |
| C67×#1278 | 2 |
| #10151 | 67 |