Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
188 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 5. C4⋊(C223⋊C8) | C4 | semidirect |
| 52. C223 | #1296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C223⋊C8) | 2 |
| #384×C223 | 2 |
| #1296 | 223 |