Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923824 | C2 | semidirect |
| 3. #24923636 | C2 | semidirect |
| 4. #24923632 | C2 | semidirect |
| 5. #24923631 | C2 | semidirect |
| 6. #24923629 | C2 | semidirect |
| 7. #24923628 | C2 | semidirect |
| 8. #24923264 | C2 | semidirect |
| 9. #24923262 | C2 | semidirect |
| 10. #97×D167 | C2 | semidirect |
| 11. #489×C167 | C2 | semidirect |
| 137. C167 | #3135 | semidirect |
| 146. #489 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| #24923818 | 2 |
| #24923636 | 2 |
| #24923632 | 2 |
| #24923631 | 2 |
| #24923629 | 2 |
| #24923628 | 2 |
| #24923264 | 2 |
| #24923262 | 2 |
| #97×D167 | 2 |
| #489×C167 | 2 |
| #3135 | 167 |