Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19128831 | C2 | semidirect |
| 3. #24923557 | C2 | direct (N × H) |
| 4. C2×#19128764 | C2 | semidirect |
| 5. C2×#19128763 | C2 | semidirect |
| 6. C2×Dic167⋊C8 | C2 | semidirect |
| 13. #19128831 | C22 | semidirect |
| 21. #19128764 | C22 | semidirect |
| 22. #19128763 | C22 | semidirect |
| 23. Dic167⋊C8 | C22 | semidirect |
| 50. C2×D4×C167 | Q8 | semidirect |
| 76. D4×C167 | C2×Q8 | semidirect |
| 101. C2×C167 | #476 | semidirect |
| 105. C167 | C2×#476 | semidirect |
| 140. C2×D4 | Dic334 | semidirect |
| 172. D4 | C2×Dic334 | semidirect |
| 207. C2 | #24923557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128831 | 2 |
| C2×D4×Dic167 | 2 |
| #24923557 | 2 |
| C2×#19128764 | 2 |
| C2×#19128763 | 2 |
| C2×Dic167⋊C8 | 2 |
| C2×#19128753 | 2 |
| C2×#102×C167 | 2 |
| C2×#476 | 167 |