Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1054 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 360 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 |
|---|---|---|
| 2. #14544503 | C2 | semidirect |
| 6. C4×#63247 | C4 | semidirect |
| 31. #10587542 | C2×C4 | semidirect |
| 32. C4×#3624 | C2×C4 | semidirect |
| 149. C17 | #20365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#63247 | 2 |
| #14544503 | 2 |
| #14544447 | 2 |
| C2×#11762654 | 2 |
| #20365 | 17 |