Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D167 | C2 | semidirect |
| 2. #24923926 | C2 | semidirect |
| 3. #24923652 | C2 | semidirect |
| 4. #24923510 | C2 | semidirect |
| 5. #24923502 | C2 | semidirect |
| 6. #24923489 | C2 | semidirect |
| 7. #24923431 | C2 | semidirect |
| 8. #24923406 | C2 | semidirect |
| 9. Q16×Dic167 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. C2×#135×C167 | C2 | semidirect |
| 74. Q16×C167 | D4 | semidirect |
| 120. C2×D167 | #135 | semidirect |
| 136. C167 | #3285 | semidirect |
| 138. C2×#135 | D167 | semidirect |
| 195. Q16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D167 | 2 |
| #24923926 | 2 |
| #24923652 | 2 |
| #24923510 | 2 |
| #24923502 | 2 |
| #24923489 | 2 |
| #24923431 | 2 |
| #24923406 | 2 |
| Q16×Dic167 | 2 |
| C8×C22⋊D167 | 2 |
| C2×#135×C167 | 2 |
| #3285 | 167 |