Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
258 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 81 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. #14545993 | C2 | semidirect |
| 2. #14545848 | C2 | semidirect |
| 3. #14545827 | C2 | semidirect |
| 4. C8×#63241 | C2 | semidirect |
| 42. #63241 | D8 | semidirect |
| 48. D136 | C16 | semidirect |
| 56. D68 | C2×C16 | semidirect |
| 64. C8×C17 | C2×C16 | semidirect |
| 110. C17 | C16×D8 | semidirect |
| 144. C8 | #10587665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545993 | 2 |
| #14545848 | 2 |
| #14545827 | 2 |
| C8×#63241 | 2 |
| #14544365 | 2 |
| C16×D8 | 17 |