Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C22×#14581937 | C2 | semidirect |
| 2. C2×#19128839 | C2 | semidirect |
| 4. #24923517 | C2 | semidirect |
| 5. #24923500 | C2 | semidirect |
| 6. #24923305 | C2 | semidirect |
| 7. #24923278 | C2 | semidirect |
| 8. #24923273 | C2 | semidirect |
| 9. #536×C167 | C2 | semidirect |
| 16. C2×#14581934 | C22 | semidirect |
| 18. C22×C167⋊C8 | C22 | semidirect |
| 24. #19128765 | C22 | semidirect |
| 25. #19128763 | C22 | semidirect |
| 26. #19128756 | C22 | semidirect |
| 33. C22⋊Q8×C167 | C22 | semidirect |
| 46. C2×C167⋊C8 | D4 | semidirect |
| 120. C167 | #3057 | semidirect |
| 124. #536 | D167 | semidirect |
| 147. C22⋊Q8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581937 | 2 |
| C2×#19128839 | 2 |
| #24923833 | 2 |
| #24923517 | 2 |
| #24923500 | 2 |
| #24923305 | 2 |
| #24923278 | 2 |
| #24923273 | 2 |
| #536×C167 | 2 |
| #3057 | 167 |