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. #24923817 | C2 | semidirect |
| 2. #24923798 | C2 | semidirect |
| 3. #24923678 | C2 | semidirect |
| 4. #24923633 | C2 | semidirect |
| 5. #24923628 | C2 | semidirect |
| 6. #24923519 | C2 | semidirect |
| 7. #24923512 | C2 | semidirect |
| 8. SD16×Dic167 | C2 | semidirect |
| 9. D8×Dic167 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #496×C167 | C2 | semidirect |
| 110. C8×C167 | #41 | semidirect |
| 137. C167 | #3171 | semidirect |
| 142. #496 | D167 | semidirect |
| 248. C8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923817 | 2 |
| #24923798 | 2 |
| #24923678 | 2 |
| #24923633 | 2 |
| #24923628 | 2 |
| #24923519 | 2 |
| #24923512 | 2 |
| SD16×Dic167 | 2 |
| D8×Dic167 | 2 |
| #24923221 | 2 |
| #496×C167 | 2 |
| #3171 | 167 |