Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 7. C22⋊(C67⋊C16) | C4 | semidirect |
| 9. #16863161 | C4 | semidirect |
| 116. C67 | #7263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561820 | 2 |
| C2×#16863161 | 2 |
| C67×#1807 | 2 |
| #7263 | 67 |