Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
508 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 132 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. C23×#63216 | C2 | semidirect |
| 2. C2×#11763707 | C2 | semidirect |
| 3. #14545011 | C2 | semidirect |
| 4. #14543838 | C2 | semidirect |
| 47. C2×#63216 | D4 | semidirect |
| 131. C22×C17 | #350 | semidirect |
| 192. C17 | #12983 | semidirect |
| 265. C22 | #11763707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63216 | 2 |
| C2×#11763707 | 2 |
| #14545011 | 2 |
| #14543838 | 2 |
| #14537479 | 2 |
| #12983 | 17 |