Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
446 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 1. C2×C4⋊#63216 | C2 | semidirect |
| 2. C2×#11763708 | C2 | semidirect |
| 3. C4×#10587538 | C2 | semidirect |
| 38. #10587538 | D4 | semidirect |
| 124. C4×C17 | #350 | semidirect |
| 179. C17 | #13193 | semidirect |
| 250. C4 | #11763708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#63216 | 2 |
| C2×#11763708 | 2 |
| C4×#10587538 | 2 |
| #14537495 | 2 |
| #13193 | 17 |