Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
708 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 708 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. #14544676 | C2 | semidirect |
| 2. #14544445 | C2 | semidirect |
| 3. #14543604 | C2 | semidirect |
| 4. #14543601 | C2 | semidirect |
| 27. C2×#63256 | C8 | semidirect |
| 63. C2×Q8×C17 | C2×C8 | semidirect |
| 81. C2×D68 | C2×C8 | semidirect |
| 272. C17 | #7578 | semidirect |
| 280. C2×Q8 | #63242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544676 | 2 |
| #14544445 | 2 |
| #14543604 | 2 |
| #14543601 | 2 |
| #14531273 | 2 |
| #7578 | 17 |