Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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. #24923231 | C2 | semidirect |
| 3. #95×D167 | C2 | semidirect |
| 4. #24923007 | C2 | semidirect |
| 5. #24923005 | C2 | semidirect |
| 6. #24923003 | C2 | semidirect |
| 7. #327×C167 | C2 | semidirect |
| 8. C2×#14581949 | C4 | semidirect |
| 13. #19128812 | C4 | semidirect |
| 15. #19128803 | C4 | semidirect |
| 19. #19128790 | C4 | semidirect |
| 29. C2×Dic334 | C2×C4 | semidirect |
| 46. C4⋊Dic167 | C2×C4 | semidirect |
| 54. C2×D4×C167 | C2×C4 | semidirect |
| 58. C4⋊C4×C167 | C2×C4 | semidirect |
| 130. C167 | #1504 | semidirect |
| 138. #327 | D167 | semidirect |
| 164. C2×D4 | C4×D167 | semidirect |
| 184. C4⋊C4 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923779 | 2 |
| #24923231 | 2 |
| #95×D167 | 2 |
| #24923007 | 2 |
| #24923005 | 2 |
| #24923003 | 2 |
| #327×C167 | 2 |
| #1504 | 167 |