Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1174 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 309 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. C22×#10587666 | C2 | semidirect |
| 2. C22×#10587665 | C2 | semidirect |
| 3. C2×#11763910 | C2 | direct (N × H) |
| 6. C2×#10587666 | C22 | semidirect |
| 8. C2×#10587665 | C22 | semidirect |
| 11. #11763910 | C22 | direct (N × H) |
| 51. #10587666 | C23 | semidirect |
| 53. #10587665 | C23 | semidirect |
| 128. C22×C17 | #350 | semidirect |
| 157. C2×C17 | C2×#350 | semidirect |
| 195. C17 | C22×#350 | semidirect |
| 271. C22 | #11763910 | direct (N × H) |
| 281. C2 | C2×#11763910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587666 | 2 |
| C22×#10587665 | 2 |
| C2×#11763910 | 2 |
| C22×#10587680 | 2 |
| C22×#350 | 17 |