Finite Group DatabasebetaFinite Group DatabasebetaOrder 28544.
160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 21. M16×C223 | C8 | semidirect |
| 59. C223 | #1283 | semidirect |
| 78. M16 | C223⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28383633 | 2 |
| C2×C4⋊(C223⋊C8) | 2 |
| C4×M16×C223 | 2 |
| #1283 | 223 |