Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923675 | C2 | semidirect |
| 3. #24923661 | C2 | semidirect |
| 4. #24923637 | C2 | semidirect |
| 5. #24923631 | C2 | semidirect |
| 6. #24923525 | C2 | semidirect |
| 8. C4×#14581940 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. C4×#14581934 | C2 | semidirect |
| 11. #533×C167 | C2 | semidirect |
| 129. C167 | #3172 | semidirect |
| 131. #533 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923803 | 2 |
| #24923675 | 2 |
| #24923661 | 2 |
| #24923637 | 2 |
| #24923631 | 2 |
| #24923525 | 2 |
| #24923517 | 2 |
| C4×#14581940 | 2 |
| C4×#14581937 | 2 |
| C4×#14581934 | 2 |
| #533×C167 | 2 |
| #3172 | 167 |