Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19128790 | C2 | semidirect |
| 3. C2×#19128754 | C2 | semidirect |
| 4. C2×#19128752 | C2 | semidirect |
| 5. C2×(C2×D167)⋊C8 | C2 | semidirect |
| 6. #24923031 | C2 | semidirect |
| 7. #340×C167 | C2 | semidirect |
| 13. #19128807 | C4 | semidirect |
| 49. C4⋊Dic167 | D4 | semidirect |
| 62. C4⋊C4×C167 | D4 | semidirect |
| 145. C167 | #1875 | semidirect |
| 153. #340 | D167 | semidirect |
| 205. C4⋊C4 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128807 | 2 |
| C2×#19128790 | 2 |
| C2×#19128754 | 2 |
| C2×#19128752 | 2 |
| C2×(C2×D167)⋊C8 | 2 |
| #24923031 | 2 |
| #340×C167 | 2 |
| #1875 | 167 |