Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14581940 | C2 | semidirect |
| 3. #24923648 | C2 | semidirect |
| 4. #24923508 | C2 | semidirect |
| 5. #24923479 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 7. #24923425 | C2 | semidirect |
| 8. #24923424 | C2 | semidirect |
| 9. C4×#14581940 | C2 | semidirect |
| 52. #14581940 | D4 | direct (N × H) |
| 100. D4×C167 | Q16 | semidirect |
| 113. C22×C167 | C2×Q16 | semidirect |
| 120. C4×C167 | C2×Q16 | semidirect |
| 130. C167 | D4×Q16 | semidirect |
| 224. D4 | #14581940 | direct (N × H) |
| 244. C22 | C2×#14581940 | semidirect |
| 254. C4 | C2×#14581940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581940 | 2 |
| D4×Dic334 | 2 |
| #24923648 | 2 |
| #24923508 | 2 |
| #24923479 | 2 |
| #24923476 | 2 |
| #24923425 | 2 |
| #24923424 | 2 |
| C4×#14581940 | 2 |
| D4×C167⋊C8 | 2 |
| D4×Q8×C167 | 2 |
| D4×Q16 | 167 |