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. C2×#19128838 | C2 | semidirect |
| 2. #24923836 | C2 | semidirect |
| 3. #24923519 | C2 | semidirect |
| 4. #24923502 | C2 | semidirect |
| 5. #24923307 | C2 | semidirect |
| 6. #24923274 | C2 | semidirect |
| 7. C22×D8×C167 | C2 | semidirect |
| 11. C2×#14581933 | C22 | semidirect |
| 12. C2×C8×D167 | C22 | semidirect |
| 15. #19128803 | C22 | semidirect |
| 18. #19128766 | C22 | semidirect |
| 19. #19128764 | C22 | semidirect |
| 20. #19128753 | C22 | semidirect |
| 49. C2×C8×C167 | D4 | semidirect |
| 93. C167 | #3058 | semidirect |
| 95. C22×D8 | D167 | semidirect |
| 139. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128838 | 2 |
| #24923836 | 2 |
| #24923519 | 2 |
| #24923502 | 2 |
| #24923307 | 2 |
| #24923274 | 2 |
| C22×D8×C167 | 2 |
| #3058 | 167 |