Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
408 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 408 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. #24923984 | C2 | semidirect |
| 2. #24923941 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923595 | C2 | semidirect |
| 5. #24923564 | C2 | semidirect |
| 6. #24923504 | C2 | semidirect |
| 7. #24923464 | C2 | semidirect |
| 8. #24923413 | C2 | semidirect |
| 9. C8×D668 | C2 | semidirect |
| 10. #24923264 | C2 | semidirect |
| 11. C4×SD16×C167 | C2 | semidirect |
| 132. C167 | #3305 | semidirect |
| 142. C4×SD16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923984 | 2 |
| #24923941 | 2 |
| #24923616 | 2 |
| #24923595 | 2 |
| #24923564 | 2 |
| #24923504 | 2 |
| #24923464 | 2 |
| #24923413 | 2 |
| C8×D668 | 2 |
| #24923264 | 2 |
| C4×SD16×C167 | 2 |
| #3305 | 167 |