Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
290 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #14545801 | C2 | semidirect |
| 4. #14545800 | C2 | semidirect |
| 49. #63241 | M16 | semidirect |
| 125. C17 | #11408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545982 | 2 |
| C2×C4×#63241 | 2 |
| #14545801 | 2 |
| #14545800 | 2 |
| #14543985 | 2 |
| #11408 | 17 |