Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19128864 | C2 | semidirect |
| 2. C2×#19128859 | C2 | semidirect |
| 3. #24923820 | C2 | semidirect |
| 4. #124×D167 | C2 | semidirect |
| 5. #24923661 | C2 | semidirect |
| 6. #24923659 | C2 | semidirect |
| 7. #24923658 | C2 | semidirect |
| 8. #24923654 | C2 | semidirect |
| 9. #24923650 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #497×C167 | C2 | semidirect |
| 17. C2×#14581940 | C22 | semidirect |
| 18. C2×#14581939 | C22 | semidirect |
| 20. C2×#14581937 | C22 | semidirect |
| 24. #19128829 | C22 | semidirect |
| 26. #19128821 | C22 | semidirect |
| 34. #19128743 | C22 | semidirect |
| 35. C8×Dic167 | C22 | semidirect |
| 36. C2×Q16×C167 | C22 | semidirect |
| 38. C4⋊Q8×C167 | C22 | semidirect |
| 40. #97×C167 | C22 | semidirect |
| 63. #14581933 | D4 | semidirect |
| 134. C167 | #3153 | semidirect |
| 141. #497 | D167 | semidirect |
| 153. C2×Q16 | C2×D167 | semidirect |
| 161. C4⋊Q8 | C2×D167 | semidirect |
| 174. #97 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128864 | 2 |
| C2×#19128859 | 2 |
| #24923820 | 2 |
| #124×D167 | 2 |
| #24923661 | 2 |
| #24923659 | 2 |
| #24923658 | 2 |
| #24923654 | 2 |
| #24923650 | 2 |
| #24923221 | 2 |
| #497×C167 | 2 |
| #3153 | 167 |