Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
558 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 99. C2×C4×C83 | Q32 | semidirect |
| 140. C83 | #13330 | semidirect |
| 241. C2×C4 | #14581738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581738 | 2 |
| C2×#19128081 | 2 |
| C2×#19127504 | 2 |
| #24905541 | 2 |
| C83×#1969 | 2 |
| #13330 | 83 |