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. #24923803 | C2 | semidirect |
| 2. #24923675 | C2 | semidirect |
| 3. #24923656 | C2 | semidirect |
| 4. #24923633 | C2 | semidirect |
| 5. #24923631 | C2 | semidirect |
| 6. #24923520 | C2 | semidirect |
| 7. #24923513 | C2 | semidirect |
| 8. C4×#14581938 | C2 | semidirect |
| 9. C4×#14581935 | C2 | semidirect |
| 10. C4×#14581934 | C2 | semidirect |
| 11. #532×C167 | C2 | semidirect |
| 91. C167⋊C8 | #41 | semidirect |
| 137. C167 | #3171 | semidirect |
| 139. #532 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| #24923675 | 2 |
| #24923656 | 2 |
| #24923633 | 2 |
| #24923631 | 2 |
| #24923520 | 2 |
| #24923513 | 2 |
| C4×#14581938 | 2 |
| C4×#14581935 | 2 |
| C4×#14581934 | 2 |
| #532×C167 | 2 |
| #3171 | 167 |