Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#19128862 | C2 | semidirect |
| 2. C2×#19128811 | C2 | semidirect |
| 3. #24923431 | C2 | semidirect |
| 4. #24923425 | C2 | semidirect |
| 5. #24923420 | C2 | semidirect |
| 6. #24923270 | C2 | semidirect |
| 7. #24923233 | C2 | semidirect |
| 9. C22×Dic334 | C22 | semidirect |
| 11. C2×#14581940 | C22 | semidirect |
| 12. C2×#14581938 | C22 | semidirect |
| 13. C2×#14581934 | C22 | semidirect |
| 17. #19128811 | C22 | semidirect |
| 18. C2×C4⋊Dic167 | C22 | semidirect |
| 21. #19128756 | C22 | semidirect |
| 22. #19128753 | C22 | semidirect |
| 24. C22⋊(C167⋊C8) | C22 | semidirect |
| 130. C22×C167 | #137 | semidirect |
| 146. C167 | #3007 | semidirect |
| 277. C22 | #19128862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128811 | 2 |
| #24923431 | 2 |
| #24923425 | 2 |
| #24923420 | 2 |
| #24923270 | 2 |
| #24923233 | 2 |
| C22×#41×C167 | 2 |
| #3007 | 167 |