Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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. #24923554 | C2 | semidirect |
| 4. #24923479 | C2 | semidirect |
| 6. #24923374 | C2 | semidirect |
| 103. C167 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| #24923599 | 2 |
| #24923554 | 2 |
| #24923479 | 2 |
| #24923425 | 2 |
| #24923374 | 2 |
| #24923326 | 2 |
| C2×C4×Q8×C167 | 2 |
| #3113 | 167 |