Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #24923817 | C2 | semidirect |
| 2. C4×#14581951 | C2 | semidirect |
| 3. #24923591 | C2 | semidirect |
| 4. #24923554 | C2 | semidirect |
| 5. #24923550 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923413 | C2 | semidirect |
| 8. #24923378 | C2 | semidirect |
| 9. #24923370 | C2 | semidirect |
| 10. #24923325 | C2 | semidirect |
| 11. #460×C167 | C2 | semidirect |
| 88. D668 | #41 | semidirect |
| 106. Q8×C167 | #41 | semidirect |
| 144. C167 | #3115 | semidirect |
| 151. #460 | D167 | semidirect |
| 233. Q8 | #14581949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923817 | 2 |
| C4×#14581951 | 2 |
| #24923591 | 2 |
| #24923554 | 2 |
| #24923550 | 2 |
| #24923461 | 2 |
| #24923413 | 2 |
| #24923378 | 2 |
| #24923370 | 2 |
| #24923325 | 2 |
| #460×C167 | 2 |
| #3115 | 167 |