Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
398 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 7. #19128106 | C4 | semidirect |
| 27. #14581726 | Q8 | semidirect |
| 102. C83 | #13275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128106 | 2 |
| C4×#14581726 | 2 |
| #24905555 | 2 |
| C2×C4⋊C16×C83 | 2 |
| #13275 | 83 |