Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
344 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #24923031 | C2 | semidirect |
| 9. C2×C4⋊Dic167 | C4 | semidirect |
| 76. C167 | #1823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic167 | 2 |
| C2×C22⋊(C167⋊C8) | 2 |
| #24923031 | 2 |
| #380×C167 | 2 |
| #1823 | 167 |