Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×D668 | C2 | semidirect |
| 2. #24923585 | C2 | semidirect |
| 3. #24923556 | C2 | semidirect |
| 4. #24923461 | C2 | semidirect |
| 5. #24923402 | C2 | semidirect |
| 6. #24923379 | C2 | semidirect |
| 7. #24923326 | C2 | semidirect |
| 8. #532×C167 | C2 | semidirect |
| 18. #19128763 | C22 | semidirect |
| 19. C4⋊(C167⋊C8) | C22 | semidirect |
| 20. #19128753 | C22 | semidirect |
| 23. #19128743 | C22 | semidirect |
| 25. C4⋊Q8×C167 | C22 | semidirect |
| 26. #127×C167 | C22 | semidirect |
| 31. C4×D4×C167 | C22 | semidirect |
| 71. D668 | #41 | semidirect |
| 120. C167 | #3109 | semidirect |
| 122. #532 | D167 | semidirect |
| 134. C4⋊Q8 | C2×D167 | semidirect |
| 135. #127 | C2×D167 | semidirect |
| 144. C4×D4 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D668 | 2 |
| #24923585 | 2 |
| #24923556 | 2 |
| #24923461 | 2 |
| #24923402 | 2 |
| #24923379 | 2 |
| #24923326 | 2 |
| #532×C167 | 2 |
| #3109 | 167 |