Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 119 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. #22562008 | C2 | semidirect |
| 2. #22558972 | C2 | semidirect |
| 3. #22558170 | C2 | semidirect |
| 8. C4×C67⋊C16 | C22 | semidirect |
| 9. #16863149 | C22 | semidirect |
| 130. C67 | #11661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562008 | 2 |
| #22558972 | 2 |
| #22558170 | 2 |
| C2×C4×D8×C67 | 2 |
| #11661 | 67 |