Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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×#19128854 | C2 | semidirect |
| 2. #24923705 | C2 | direct (N × H) |
| 3. C2×#19128776 | C2 | semidirect |
| 4. C2×#19128773 | C2 | semidirect |
| 5. C2×#19128772 | C2 | semidirect |
| 6. C22×D8×C167 | C2 | semidirect |
| 9. #19128854 | C22 | semidirect |
| 10. C2×Dic668 | C22 | semidirect |
| 12. C2×D1336 | C22 | semidirect |
| 13. #19128776 | C22 | semidirect |
| 14. #19128773 | C22 | semidirect |
| 15. #19128772 | C22 | semidirect |
| 16. C2×C167⋊C16 | C22 | semidirect |
| 21. C2×D8×C167 | C22 | semidirect |
| 30. Dic668 | C23 | semidirect |
| 33. D1336 | C23 | semidirect |
| 34. C167⋊C16 | C23 | semidirect |
| 84. C2×C167 | #509 | semidirect |
| 87. C167 | C2×#509 | semidirect |
| 90. C22×D8 | D167 | semidirect |
| 105. C2×D8 | C2×D167 | semidirect |
| 173. C2 | #24923705 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| #24923705 | 2 |
| C2×#19128776 | 2 |
| C2×#19128773 | 2 |
| C2×#19128772 | 2 |
| C22×D8×C167 | 2 |
| C2×#509 | 167 |