Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
690 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 229 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×#11763930 | C2 | semidirect |
| 2. #14546000 | C2 | semidirect |
| 3. D4×#63241 | C2 | semidirect |
| 4. #14545973 | C2 | semidirect |
| 5. #14545955 | C2 | semidirect |
| 6. C4×#10587665 | C2 | semidirect |
| 41. #10587665 | D4 | semidirect |
| 116. C4×C17 | #504 | semidirect |
| 169. C17 | #33434 | semidirect |
| 230. C4 | #11763930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763930 | 2 |
| #14546000 | 2 |
| D4×#63241 | 2 |
| #14545973 | 2 |
| #14545955 | 2 |
| C4×#10587665 | 2 |
| #14545506 | 2 |
| #33434 | 17 |