Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
518 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 98 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×#10587536 | C2 | semidirect |
| 2. C2×#11763724 | C2 | semidirect |
| 3. #14545009 | C2 | semidirect |
| 4. #14543845 | C2 | semidirect |
| 57. #10587536 | D4 | semidirect |
| 171. C22×C17 | #359 | semidirect |
| 263. C17 | #12990 | semidirect |
| 374. C22 | #11763724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587536 | 2 |
| C2×#11763724 | 2 |
| #14545009 | 2 |
| #14543845 | 2 |
| #14538367 | 2 |
| #12990 | 17 |