Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
434 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 168. C83 | #10143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918665 | 2 |
| C2×#19128107 | 2 |
| #24906189 | 2 |
| #24906078 | 2 |
| #24905818 | 2 |
| #24905363 | 2 |
| C83×#3229 | 2 |
| #10143 | 83 |