Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24923888 | C2 | semidirect |
| 2. #24923667 | C2 | semidirect |
| 3. #24923628 | C2 | semidirect |
| 4. #24923524 | C2 | semidirect |
| 6. #24923495 | C2 | semidirect |
| 7. #24923381 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. SD16×Dic167 | C2 | semidirect |
| 10. #24923223 | C2 | semidirect |
| 11. #495×C167 | C2 | semidirect |
| 109. C167 | #3173 | semidirect |
| 113. #495 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923888 | 2 |
| #24923667 | 2 |
| #24923628 | 2 |
| #24923524 | 2 |
| #24923519 | 2 |
| #24923495 | 2 |
| #24923381 | 2 |
| #24923376 | 2 |
| SD16×Dic167 | 2 |
| #24923223 | 2 |
| #495×C167 | 2 |
| #3173 | 167 |