Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 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. #24923678 | C2 | semidirect |
| 4. #24923637 | C2 | semidirect |
| 5. #24923628 | C2 | semidirect |
| 6. #24923524 | C2 | semidirect |
| 8. Q16×Dic167 | C2 | semidirect |
| 9. SD16×Dic167 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #497×C167 | C2 | semidirect |
| 129. C167 | #3172 | semidirect |
| 134. #497 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923824 | 2 |
| #24923798 | 2 |
| #24923678 | 2 |
| #24923637 | 2 |
| #24923628 | 2 |
| #24923524 | 2 |
| #24923512 | 2 |
| Q16×Dic167 | 2 |
| SD16×Dic167 | 2 |
| #24923221 | 2 |
| #497×C167 | 2 |
| #3172 | 167 |