Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24923608 | C2 | semidirect |
| 4. #24923564 | C2 | semidirect |
| 5. #24923560 | C2 | semidirect |
| 6. #24923471 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. #24923372 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #462×C167 | C2 | semidirect |
| 136. C167 | #3116 | semidirect |
| 143. #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×#14581951 | 2 |
| #24923608 | 2 |
| #24923564 | 2 |
| #24923560 | 2 |
| #24923471 | 2 |
| #24923430 | 2 |
| #24923376 | 2 |
| #24923372 | 2 |
| #24923325 | 2 |
| #462×C167 | 2 |
| #3116 | 167 |