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. #24923613 | C2 | semidirect |
| 4. #24923561 | C2 | semidirect |
| 5. #24923480 | C2 | semidirect |
| 6. #24923474 | C2 | semidirect |
| 8. #24923375 | C2 | semidirect |
| 9. #24923366 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #476×C167 | C2 | semidirect |
| 136. C167 | #3116 | semidirect |
| 142. #476 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| C4×#14581949 | 2 |
| #24923613 | 2 |
| #24923561 | 2 |
| #24923480 | 2 |
| #24923474 | 2 |
| #24923432 | 2 |
| #24923375 | 2 |
| #24923366 | 2 |
| #24923325 | 2 |
| #476×C167 | 2 |
| #3116 | 167 |