Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19128851 | C2 | semidirect |
| 2. #24923923 | C2 | semidirect |
| 3. #24923649 | C2 | semidirect |
| 4. #24923511 | C2 | semidirect |
| 5. #24923474 | C2 | semidirect |
| 6. #24923432 | C2 | semidirect |
| 7. C8×D668 | C2 | semidirect |
| 8. C4×D8×C167 | C2 | semidirect |
| 49. D8×C167 | D4 | semidirect |
| 85. C4×C167 | #135 | semidirect |
| 95. C167 | #3283 | semidirect |
| 103. C4×D8 | D167 | semidirect |
| 137. D8 | D668 | semidirect |
| 183. C4 | #19128851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128851 | 2 |
| #24923923 | 2 |
| #24923649 | 2 |
| #24923511 | 2 |
| #24923474 | 2 |
| #24923432 | 2 |
| C8×D668 | 2 |
| C4×D8×C167 | 2 |
| #3283 | 167 |