Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14581938 | C2 | semidirect |
| 2. C2×C4×Dic334 | C2 | semidirect |
| 3. #24923466 | C2 | direct (N × H) |
| 4. C2×C4⋊(C167⋊C8) | C2 | semidirect |
| 5. C2×#19128753 | C2 | semidirect |
| 9. C2×#14581938 | C22 | semidirect |
| 12. C4×Dic334 | C22 | semidirect |
| 16. C4⋊(C167⋊C8) | C22 | semidirect |
| 17. #19128753 | C22 | semidirect |
| 26. C2×Dic334 | D4 | semidirect |
| 53. Dic334 | C2×D4 | semidirect |
| 70. C2×C4×C167 | SD16 | semidirect |
| 87. C4×C167 | C2×SD16 | semidirect |
| 93. C2×C167 | #460 | semidirect |
| 97. C167 | C2×#460 | semidirect |
| 167. C2×C4 | #14581938 | semidirect |
| 187. C4 | C2×#14581938 | semidirect |
| 191. C2 | #24923466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581938 | 2 |
| C2×C4×Dic334 | 2 |
| #24923466 | 2 |
| C2×C4⋊(C167⋊C8) | 2 |
| C2×#19128753 | 2 |
| C2×#127×C167 | 2 |
| C2×#460 | 167 |