Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19128855 | C2 | semidirect |
| 2. C2×#19128854 | C2 | semidirect |
| 3. #24923921 | C2 | semidirect |
| 4. #24923647 | C2 | semidirect |
| 5. #24923511 | C2 | semidirect |
| 6. #24923473 | C2 | semidirect |
| 7. #24923434 | C2 | semidirect |
| 8. #24923429 | C2 | semidirect |
| 9. #24923351 | C2 | semidirect |
| 10. C8×C22⋊D167 | C2 | semidirect |
| 11. #467×C167 | C2 | semidirect |
| 58. D1336 | D4 | semidirect |
| 129. Dic167 | #135 | semidirect |
| 136. C167 | #3283 | semidirect |
| 143. #467 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128855 | 2 |
| C2×#19128854 | 2 |
| #24923921 | 2 |
| #24923647 | 2 |
| #24923511 | 2 |
| #24923473 | 2 |
| #24923434 | 2 |
| #24923429 | 2 |
| #24923351 | 2 |
| C8×C22⋊D167 | 2 |
| #467×C167 | 2 |
| #3283 | 167 |