Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
384 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #22558970 | C2 | semidirect |
| 4. #22558565 | C2 | semidirect |
| 6. #22558496 | C2 | semidirect |
| 7. C67×#1528 | C2 | semidirect |
| 177. #1528 | D67 | semidirect |
| 182. C67 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863753 | 2 |
| #22558970 | 2 |
| #22558806 | 2 |
| #22558565 | 2 |
| #22558562 | 2 |
| #22558496 | 2 |
| C67×#1528 | 2 |
| #9790 | 67 |