Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #24923984 | C2 | semidirect |
| 2. #24923615 | C2 | semidirect |
| 3. #24923590 | C2 | semidirect |
| 4. #24923564 | C2 | semidirect |
| 5. #24923503 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923414 | C2 | semidirect |
| 8. C4×#14581937 | C2 | semidirect |
| 9. D4×C167⋊C8 | C2 | semidirect |
| 10. #24923265 | C2 | semidirect |
| 11. #550×C167 | C2 | semidirect |
| 132. C167 | #3305 | semidirect |
| 135. #550 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923984 | 2 |
| #24923615 | 2 |
| #24923590 | 2 |
| #24923564 | 2 |
| #24923503 | 2 |
| #24923461 | 2 |
| #24923414 | 2 |
| C4×#14581937 | 2 |
| D4×C167⋊C8 | 2 |
| #24923265 | 2 |
| #550×C167 | 2 |
| #3305 | 167 |