Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
254 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 19. #10587538 | C8 | semidirect |
| 23. C2×#63216 | C8 | semidirect |
| 124. C17 | #7141 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10587538 | 2 |
| C2×C4×#63216 | 2 |
| #14527068 | 2 |
| #7141 | 17 |