Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
312 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C2×#19128755 | C2 | semidirect |
| 4. C2×#19128750 | C2 | semidirect |
| 5. #24923038 | C2 | semidirect |
| 6. #24923033 | C2 | semidirect |
| 10. #19128862 | C4 | semidirect |
| 116. C167 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128839 | 2 |
| C2×#19128755 | 2 |
| C2×#19128750 | 2 |
| #24923038 | 2 |
| #24923033 | 2 |
| #417×C167 | 2 |
| #1908 | 167 |