Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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×D1336 | C2 | semidirect |
| 2. C2×#19128838 | C2 | semidirect |
| 3. #24923838 | C2 | semidirect |
| 4. #24923523 | C2 | semidirect |
| 5. #24923506 | C2 | semidirect |
| 6. #24923273 | C2 | semidirect |
| 7. #427×C167 | C2 | semidirect |
| 15. C2×#14581933 | C22 | semidirect |
| 16. C2×C8×D167 | C22 | semidirect |
| 19. #19128807 | C22 | semidirect |
| 21. #19128752 | C22 | semidirect |
| 24. #107×C167 | C22 | semidirect |
| 25. #106×C167 | C22 | semidirect |
| 46. C2×C8×C167 | D4 | semidirect |
| 93. C167 | #3058 | semidirect |
| 100. #427 | D167 | semidirect |
| 117. #107 | C2×D167 | semidirect |
| 118. #106 | C2×D167 | semidirect |
| 139. C2×C8 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1336 | 2 |
| C2×#19128838 | 2 |
| #24923838 | 2 |
| #24923523 | 2 |
| #24923506 | 2 |
| #24923273 | 2 |
| #427×C167 | 2 |
| #3058 | 167 |