Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
410 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 72. C2×C4×C83 | Q32 | semidirect |
| 114. C83 | #13450 | semidirect |
| 191. C2×C4 | Dic664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic664 | 2 |
| C2×#19127506 | 2 |
| #24908324 | 2 |
| #24905555 | 2 |
| C2×C4⋊C16×C83 | 2 |
| #13450 | 83 |