Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
422 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 114 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. #14545145 | C2 | semidirect |
| 2. #14545141 | C2 | semidirect |
| 3. D4⋊#63216 | C2 | semidirect |
| 6. C4⋊#63216 | C22 | semidirect |
| 10. C4×#63216 | C22 | semidirect |
| 171. C17 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545145 | 2 |
| #14545141 | 2 |
| D4⋊#63216 | 2 |
| C2×D4×#3622 | 2 |
| #11631 | 17 |