Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
554 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 121 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×#10587670 | C2 | semidirect |
| 2. C2×C22⋊#63241 | C2 | semidirect |
| 3. C2×C22⋊#63241 | C2 | semidirect |
| 4. #14545854 | C2 | semidirect |
| 42. C2×#63241 | D4 | semidirect |
| 105. C23×C17 | M32 | semidirect |
| 110. C2×C4×C17 | M32 | semidirect |
| 215. C17 | #12977 | semidirect |
| 265. C23 | #10587670 | semidirect |
| 287. C2×C4 | #10587670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587670 | 2 |
| C2×C22⋊#63241 | 2 |
| #14545854 | 2 |
| C2×D4×#3624 | 2 |
| #12977 | 17 |