Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19128861 | C2 | semidirect |
| 2. #24923934 | C2 | semidirect |
| 4. #24923648 | C2 | semidirect |
| 5. #24923526 | C2 | semidirect |
| 6. #24923480 | C2 | semidirect |
| 7. #24923428 | C2 | semidirect |
| 8. #24923426 | C2 | semidirect |
| 9. C4×#14581938 | C2 | semidirect |
| 10. #24923346 | C2 | semidirect |
| 11. #461×C167 | C2 | semidirect |
| 57. #14581938 | D4 | semidirect |
| 122. C4×C167 | #137 | semidirect |
| 134. C167 | #3276 | semidirect |
| 142. #461 | D167 | semidirect |
| 261. C4 | #19128861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128861 | 2 |
| #24923934 | 2 |
| #24923923 | 2 |
| #24923648 | 2 |
| #24923526 | 2 |
| #24923480 | 2 |
| #24923428 | 2 |
| #24923426 | 2 |
| C4×#14581938 | 2 |
| #24923346 | 2 |
| #461×C167 | 2 |
| #3276 | 167 |