Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
300 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 18. #14581703 | C8 | semidirect |
| 107. C83 | #7023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C83⋊C8) | 2 |
| #24907212 | 2 |
| C83×#1839 | 2 |
| #7023 | 83 |