Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #24923668 | C2 | semidirect |
| 3. #24923643 | C2 | semidirect |
| 4. #24923637 | C2 | semidirect |
| 5. #24923635 | C2 | semidirect |
| 6. #24923517 | C2 | semidirect |
| 7. #24923500 | C2 | semidirect |
| 8. #24923367 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. #24923225 | C2 | semidirect |
| 11. #541×C167 | C2 | semidirect |
| 108. C167 | #3174 | semidirect |
| 110. #541 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923874 | 2 |
| #24923668 | 2 |
| #24923643 | 2 |
| #24923637 | 2 |
| #24923635 | 2 |
| #24923517 | 2 |
| #24923500 | 2 |
| #24923367 | 2 |
| C4×#14581937 | 2 |
| #24923225 | 2 |
| #541×C167 | 2 |
| #3174 | 167 |