Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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. #14541177 | C2 | semidirect |
| 2. #14531007 | C2 | semidirect |
| 3. #14530821 | C2 | semidirect |
| 4. #14526843 | C2 | semidirect |
| 5. #14526747 | C2 | semidirect |
| 6. D4⋊#63214 | C2 | semidirect |
| 95. D4×C17 | SD32 | semidirect |
| 187. C17 | #12342 | semidirect |
| 232. D4 | #10587498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14541177 | 2 |
| #14531007 | 2 |
| #14530821 | 2 |
| #14526843 | 2 |
| #14526747 | 2 |
| D4⋊#63214 | 2 |
| C17×#1667 | 2 |
| #12342 | 17 |