Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
490 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 163 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 |
|---|---|---|
| 2. #24909616 | C2 | semidirect |
| 4. #24909514 | C2 | semidirect |
| 71. C2×C4×C83 | Q32 | semidirect |
| 106. C83 | #33815 | semidirect |
| 177. C2×C4 | Dic664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918049 | 2 |
| #24909616 | 2 |
| #24909554 | 2 |
| #24909514 | 2 |
| C2×C4⋊C16×C83 | 2 |
| #33815 | 83 |