Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×#19128863 | C2 | semidirect |
| 3. #24923648 | C2 | semidirect |
| 4. #24923525 | C2 | semidirect |
| 5. #24923479 | C2 | semidirect |
| 6. #24923471 | C2 | semidirect |
| 7. #24923429 | C2 | semidirect |
| 8. #24923425 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. #24923347 | C2 | semidirect |
| 11. D4×Q8×C167 | C2 | semidirect |
| 53. #14581937 | D4 | semidirect |
| 124. C4×C167 | #137 | semidirect |
| 134. C167 | #3276 | semidirect |
| 137. D4×Q8 | D167 | semidirect |
| 261. C4 | #19128863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| #24923924 | 2 |
| #24923648 | 2 |
| #24923525 | 2 |
| #24923479 | 2 |
| #24923471 | 2 |
| #24923429 | 2 |
| #24923425 | 2 |
| C4×#14581937 | 2 |
| #24923347 | 2 |
| D4×Q8×C167 | 2 |
| #3276 | 167 |