Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
406 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 1. #24923992 | C2 | semidirect |
| 2. #24923941 | C2 | semidirect |
| 3. #24923658 | C2 | semidirect |
| 4. #24923642 | C2 | semidirect |
| 5. #24923485 | C2 | semidirect |
| 6. #24923475 | C2 | semidirect |
| 7. #24923470 | C2 | semidirect |
| 8. #24923465 | C2 | semidirect |
| 9. #24923371 | C2 | semidirect |
| 10. C4×D1336 | C2 | semidirect |
| 11. #446×C167 | C2 | semidirect |
| 106. C8×C167 | #41 | semidirect |
| 132. C167 | #3397 | semidirect |
| 142. #446 | D167 | semidirect |
| 239. C8 | #14581951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923941 | 2 |
| #24923658 | 2 |
| #24923642 | 2 |
| #24923485 | 2 |
| #24923475 | 2 |
| #24923470 | 2 |
| #24923465 | 2 |
| #24923371 | 2 |
| C4×D1336 | 2 |
| #446×C167 | 2 |
| #3397 | 167 |