Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 10. #16863224 | C4 | semidirect |
| 57. C16×C67 | C4⋊C4 | semidirect |
| 104. C67 | #13167 | semidirect |
| 156. C16 | Dic67⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863224 | 2 |
| C2×#16863171 | 2 |
| #22560940 | 2 |
| #22558300 | 2 |
| C2×#366×C67 | 2 |
| #13167 | 67 |