Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19128862 | C2 | semidirect |
| 2. C2×#19128857 | C2 | semidirect |
| 3. C2×#19128820 | C2 | semidirect |
| 4. #24923661 | C2 | semidirect |
| 5. #24923656 | C2 | semidirect |
| 6. #24923651 | C2 | semidirect |
| 7. C4×#14581934 | C2 | semidirect |
| 8. #532×C167 | C2 | semidirect |
| 13. C2×#14581940 | C22 | semidirect |
| 14. C2×#14581938 | C22 | semidirect |
| 22. #19128743 | C22 | semidirect |
| 23. C4×C167⋊C8 | C22 | semidirect |
| 25. C4⋊Q8×C167 | C22 | semidirect |
| 26. #127×C167 | C22 | semidirect |
| 27. #124×C167 | C22 | semidirect |
| 43. #14581934 | D4 | semidirect |
| 106. C167 | #3153 | semidirect |
| 110. #532 | D167 | semidirect |
| 126. C4⋊Q8 | C2×D167 | semidirect |
| 127. #127 | C2×D167 | semidirect |
| 131. #124 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128862 | 2 |
| C2×#19128857 | 2 |
| C2×#19128820 | 2 |
| #24923661 | 2 |
| #24923656 | 2 |
| #24923651 | 2 |
| C4×#14581934 | 2 |
| #532×C167 | 2 |
| #3153 | 167 |