Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 149 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. #24923674 | C2 | semidirect |
| 3. #24923649 | C2 | semidirect |
| 4. #24923620 | C2 | semidirect |
| 6. C4×Dic668 | C2 | semidirect |
| 52. C2×C4×C167 | Q16 | semidirect |
| 77. C167 | #3170 | semidirect |
| 130. C2×C4 | Dic668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| #24923674 | 2 |
| #24923649 | 2 |
| #24923620 | 2 |
| #24923510 | 2 |
| C4×Dic668 | 2 |
| C2×C4×C8×C167 | 2 |
| #3170 | 167 |