Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19128854 | C2 | semidirect |
| 2. C22×C8×D167 | C2 | semidirect |
| 3. #24923781 | C2 | semidirect |
| 4. #24923511 | C2 | semidirect |
| 5. #24923506 | C2 | semidirect |
| 6. #24923499 | C2 | semidirect |
| 7. #24923263 | C2 | semidirect |
| 8. #427×C167 | C2 | semidirect |
| 12. C2×Dic668 | C22 | semidirect |
| 13. C2×#14581939 | C22 | semidirect |
| 14. C2×D1336 | C22 | semidirect |
| 24. #19128755 | C22 | semidirect |
| 25. #19128752 | C22 | semidirect |
| 28. #107×C167 | C22 | semidirect |
| 29. #106×C167 | C22 | semidirect |
| 54. C2×C8×C167 | D4 | semidirect |
| 94. C2×D167 | #135 | semidirect |
| 106. C167 | #3050 | semidirect |
| 114. #427 | D167 | semidirect |
| 133. #107 | C2×D167 | semidirect |
| 134. #106 | C2×D167 | semidirect |
| 158. C2×C8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128854 | 2 |
| C22×C8×D167 | 2 |
| #24923781 | 2 |
| #24923511 | 2 |
| #24923506 | 2 |
| #24923499 | 2 |
| #24923263 | 2 |
| #427×C167 | 2 |
| #3050 | 167 |