Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. #24923820 | C2 | semidirect |
| 3. C4×#14581951 | C2 | semidirect |
| 4. #24923493 | C2 | semidirect |
| 5. #24923487 | C2 | semidirect |
| 6. #24923471 | C2 | semidirect |
| 7. #24923469 | C2 | semidirect |
| 8. #24923465 | C2 | semidirect |
| 9. C4⋊C8×D167 | C2 | semidirect |
| 10. #24923264 | C2 | semidirect |
| 11. #462×C167 | C2 | semidirect |
| 47. #14581951 | D4 | semidirect |
| 137. C4×C167 | #135 | semidirect |
| 150. C167 | #3035 | semidirect |
| 157. #462 | D167 | semidirect |
| 292. C4 | #19128855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128855 | 2 |
| #24923820 | 2 |
| C4×#14581951 | 2 |
| #24923493 | 2 |
| #24923487 | 2 |
| #24923471 | 2 |
| #24923469 | 2 |
| #24923465 | 2 |
| C4⋊C8×D167 | 2 |
| #24923264 | 2 |
| #462×C167 | 2 |
| #3035 | 167 |