Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#19128763 | C2 | semidirect |
| 4. #24923165 | C2 | semidirect |
| 5. #24923032 | C2 | semidirect |
| 6. #24923023 | C2 | semidirect |
| 18. #19128753 | C4 | semidirect |
| 33. C2×C167⋊C8 | C2×C4 | semidirect |
| 36. C4⋊Dic167 | C2×C4 | semidirect |
| 81. D4×C167 | C4⋊C4 | semidirect |
| 123. C167 | #1864 | semidirect |
| 191. D4 | Dic167⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic167 | 2 |
| C2×#19128763 | 2 |
| C2×#19128753 | 2 |
| #24923165 | 2 |
| #24923032 | 2 |
| #24923023 | 2 |
| C2×#102×C167 | 2 |
| #1864 | 167 |