Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128855 | C2 | semidirect |
| 2. #24923930 | C2 | semidirect |
| 3. #24923654 | C2 | semidirect |
| 4. #24923507 | C2 | semidirect |
| 5. #24923505 | C2 | semidirect |
| 6. #24923493 | C2 | semidirect |
| 7. #24923430 | C2 | semidirect |
| 8. #24923408 | C2 | semidirect |
| 9. Q16×Dic167 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. C22×Q16×C167 | C2 | semidirect |
| 76. Q16×C167 | D4 | semidirect |
| 113. C22×C167 | #135 | semidirect |
| 136. C167 | #3285 | semidirect |
| 139. C22×Q16 | D167 | semidirect |
| 195. Q16 | C22⋊D167 | semidirect |
| 256. C22 | #19128855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128855 | 2 |
| #24923930 | 2 |
| #24923654 | 2 |
| #24923507 | 2 |
| #24923505 | 2 |
| #24923493 | 2 |
| #24923430 | 2 |
| #24923408 | 2 |
| Q16×Dic167 | 2 |
| C8×C22⋊D167 | 2 |
| C22×Q16×C167 | 2 |
| #3285 | 167 |