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. #24923893 | C2 | semidirect |
| 2. #24923653 | C2 | semidirect |
| 3. #24923631 | C2 | semidirect |
| 4. #24923528 | C2 | semidirect |
| 6. #24923499 | C2 | semidirect |
| 7. #24923380 | C2 | semidirect |
| 8. #24923375 | C2 | semidirect |
| 9. #24923356 | C2 | semidirect |
| 10. #24923223 | C2 | semidirect |
| 11. #498×C167 | C2 | semidirect |
| 109. C167 | #3173 | semidirect |
| 112. #498 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923893 | 2 |
| #24923653 | 2 |
| #24923631 | 2 |
| #24923528 | 2 |
| #24923523 | 2 |
| #24923499 | 2 |
| #24923380 | 2 |
| #24923375 | 2 |
| #24923356 | 2 |
| #24923223 | 2 |
| #498×C167 | 2 |
| #3173 | 167 |