Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 80. C2×Dic166 | Q16 | semidirect |
| 188. C83 | #10183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917264 | 2 |
| C2×#19127993 | 2 |
| #24906148 | 2 |
| #24905866 | 2 |
| #24905786 | 2 |
| #24905359 | 2 |
| C83×#3209 | 2 |
| #10183 | 83 |