Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 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. #24923820 | C2 | semidirect |
| 2. #24923804 | C2 | semidirect |
| 3. #24923658 | C2 | semidirect |
| 4. #24923635 | C2 | semidirect |
| 5. #24923631 | C2 | semidirect |
| 6. #24923523 | C2 | semidirect |
| 7. #24923516 | C2 | semidirect |
| 8. #24923356 | C2 | semidirect |
| 9. #24923351 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #501×C167 | C2 | semidirect |
| 110. C8×C167 | #41 | semidirect |
| 137. C167 | #3171 | semidirect |
| 141. #501 | D167 | semidirect |
| 248. C8 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923820 | 2 |
| #24923804 | 2 |
| #24923658 | 2 |
| #24923635 | 2 |
| #24923631 | 2 |
| #24923523 | 2 |
| #24923516 | 2 |
| #24923356 | 2 |
| #24923351 | 2 |
| #24923221 | 2 |
| #501×C167 | 2 |
| #3171 | 167 |