Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923608 | C2 | semidirect |
| 4. #24923602 | C2 | semidirect |
| 5. #24923595 | C2 | semidirect |
| 6. #24923588 | C2 | semidirect |
| 7. #24923582 | C2 | semidirect |
| 8. #24923304 | C2 | semidirect |
| 9. #24923264 | C2 | semidirect |
| 10. C22⋊C8×D167 | C2 | semidirect |
| 11. #483×C167 | C2 | semidirect |
| 30. #19128765 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. #19128764 | C22 | semidirect |
| 33. #19128756 | C22 | semidirect |
| 34. #19128754 | C22 | semidirect |
| 35. #19128752 | C22 | semidirect |
| 40. #106×C167 | C22 | semidirect |
| 41. #103×C167 | C22 | semidirect |
| 143. C167 | #3091 | semidirect |
| 149. #483 | D167 | semidirect |
| 179. #106 | C2×D167 | semidirect |
| 181. #103 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923782 | 2 |
| C2×#19128790 | 2 |
| #24923608 | 2 |
| #24923602 | 2 |
| #24923595 | 2 |
| #24923588 | 2 |
| #24923582 | 2 |
| #24923304 | 2 |
| #24923264 | 2 |
| C22⋊C8×D167 | 2 |
| #483×C167 | 2 |
| #3091 | 167 |