Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
4070 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 4070 conjugacy classes of subgroups — too many to draw. Only its 456 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×#10587543 | C2 | semidirect |
| 2. C22×C22⋊#3624 | C2 | semidirect |
| 3. #14544608 | C2 | direct (N × H) |
| 7. C2×#10587543 | C22 | semidirect |
| 9. C2×C22⋊#3624 | C22 | semidirect |
| 178. C2×C17 | #1780 | semidirect |
| 217. C17 | C2×#1780 | semidirect |
| 325. C2 | #14544608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587543 | 2 |
| C22×C22⋊#3624 | 2 |
| #14544608 | 2 |
| C23×#63254 | 2 |
| C2×#1780 | 17 |