Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1870 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 1870 conjugacy classes of subgroups — too many to draw. Only its 256 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×#11763829 | C2 | semidirect |
| 2. #14544311 | C2 | direct (N × H) |
| 3. C2×#11763667 | C2 | semidirect |
| 6. #11763829 | C22 | semidirect |
| 7. C2×#10587544 | C22 | semidirect |
| 10. #11763667 | C22 | semidirect |
| 56. #10587544 | C23 | semidirect |
| 190. C2×C17 | #1555 | semidirect |
| 231. C17 | C2×#1555 | semidirect |
| 344. C2 | #14544311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763829 | 2 |
| #14544311 | 2 |
| C2×#11763667 | 2 |
| C22×#10587626 | 2 |
| C2×#1555 | 17 |