Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #24923555 | C2 | semidirect |
| 5. #24923554 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. #24923373 | C2 | semidirect |
| 11. #462×C167 | C2 | semidirect |
| 132. C167 | #3113 | semidirect |
| 140. #462 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| C4×Q8×D167 | 2 |
| #24923598 | 2 |
| #24923555 | 2 |
| #24923554 | 2 |
| #24923476 | 2 |
| #24923423 | 2 |
| #24923376 | 2 |
| #24923373 | 2 |
| #24923325 | 2 |
| #462×C167 | 2 |
| #3113 | 167 |