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. #24923882 | C2 | semidirect |
| 3. #24923642 | C2 | semidirect |
| 4. #24923639 | C2 | semidirect |
| 5. #24923635 | C2 | semidirect |
| 6. #24923516 | C2 | semidirect |
| 7. #24923499 | C2 | semidirect |
| 8. #24923368 | C2 | semidirect |
| 9. #24923356 | C2 | semidirect |
| 10. #24923223 | C2 | semidirect |
| 11. #499×C167 | C2 | semidirect |
| 108. C167 | #3174 | semidirect |
| 112. #499 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923882 | 2 |
| #24923875 | 2 |
| #24923642 | 2 |
| #24923639 | 2 |
| #24923635 | 2 |
| #24923516 | 2 |
| #24923499 | 2 |
| #24923368 | 2 |
| #24923356 | 2 |
| #24923223 | 2 |
| #499×C167 | 2 |
| #3174 | 167 |