Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19128767 | C2 | semidirect |
| 3. #24923296 | C2 | semidirect |
| 6. #24923024 | C2 | semidirect |
| 7. #339×C167 | C2 | semidirect |
| 20. #19128755 | C4 | semidirect |
| 21. #19128755 | C4 | semidirect |
| 22. #19128752 | C4 | semidirect |
| 23. #19128752 | C4 | semidirect |
| 109. C167 | #1866 | semidirect |
| 116. #339 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128840 | 2 |
| C2×#19128767 | 2 |
| #24923296 | 2 |
| C2×#19128760 | 2 |
| #24923263 | 2 |
| #24923024 | 2 |
| #339×C167 | 2 |
| #1866 | 167 |