Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
482 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 482 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. C2×#19128854 | C2 | semidirect |
| 2. C2×Q16×D167 | C2 | semidirect |
| 3. #24923929 | C2 | semidirect |
| 4. #24923654 | C2 | semidirect |
| 5. #24923506 | C2 | semidirect |
| 6. #24923494 | C2 | semidirect |
| 7. #24923429 | C2 | semidirect |
| 8. #24923409 | C2 | semidirect |
| 9. #24923363 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. #467×C167 | C2 | semidirect |
| 54. Dic668 | D4 | semidirect |
| 120. C2×D167 | #135 | semidirect |
| 136. C167 | #3285 | semidirect |
| 142. #467 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| C2×Q16×D167 | 2 |
| #24923929 | 2 |
| #24923654 | 2 |
| #24923506 | 2 |
| #24923494 | 2 |
| #24923429 | 2 |
| #24923409 | 2 |
| #24923363 | 2 |
| C8×C22⋊D167 | 2 |
| #467×C167 | 2 |
| #3285 | 167 |