Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923820 | C2 | semidirect |
| 2. #24923798 | C2 | semidirect |
| 3. #24923675 | C2 | semidirect |
| 4. #24923659 | C2 | semidirect |
| 5. #24923634 | C2 | semidirect |
| 6. #24923521 | C2 | semidirect |
| 7. #24923518 | C2 | semidirect |
| 8. #24923354 | C2 | semidirect |
| 9. #24923349 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #489×C167 | C2 | semidirect |
| 100. C167⋊C8 | #41 | semidirect |
| 137. C167 | #3171 | semidirect |
| 144. #489 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923820 | 2 |
| #24923798 | 2 |
| #24923675 | 2 |
| #24923659 | 2 |
| #24923634 | 2 |
| #24923521 | 2 |
| #24923518 | 2 |
| #24923354 | 2 |
| #24923349 | 2 |
| #24923221 | 2 |
| #489×C167 | 2 |
| #3171 | 167 |