Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D668 | C2 | semidirect |
| 3. #24923629 | C2 | semidirect |
| 4. #24923620 | C2 | semidirect |
| 5. #24923565 | C2 | semidirect |
| 6. #24923550 | C2 | semidirect |
| 8. #24923475 | C2 | semidirect |
| 9. #24923371 | C2 | semidirect |
| 11. #446×C167 | C2 | semidirect |
| 122. C167 | #3367 | semidirect |
| 132. #446 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| Q8×D668 | 2 |
| #24923629 | 2 |
| #24923620 | 2 |
| #24923565 | 2 |
| #24923550 | 2 |
| #24923485 | 2 |
| #24923475 | 2 |
| #24923371 | 2 |
| C4×D1336 | 2 |
| #446×C167 | 2 |
| #3367 | 167 |