Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C2×#19128742 | C2 | semidirect |
| 5. #24923033 | C2 | semidirect |
| 6. #24923028 | C2 | semidirect |
| 7. #424×C167 | C2 | semidirect |
| 13. #19128755 | C4 | semidirect |
| 14. #19128752 | C4 | semidirect |
| 90. C167 | #1938 | semidirect |
| 92. #424 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128758 | 2 |
| #24923263 | 2 |
| #24923235 | 2 |
| C2×#19128742 | 2 |
| #24923033 | 2 |
| #24923028 | 2 |
| #424×C167 | 2 |
| #1938 | 167 |