Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #24923825 | C2 | semidirect |
| 3. #24923626 | C2 | semidirect |
| 4. #24923624 | C2 | semidirect |
| 5. #24923623 | C2 | semidirect |
| 6. #24923618 | C2 | semidirect |
| 7. #24923614 | C2 | semidirect |
| 8. #24923264 | C2 | semidirect |
| 9. #24923262 | C2 | semidirect |
| 10. C4×C8×D167 | C2 | semidirect |
| 11. #488×C167 | C2 | semidirect |
| 114. C167 | #3131 | semidirect |
| 121. #488 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923825 | 2 |
| #24923818 | 2 |
| #24923626 | 2 |
| #24923624 | 2 |
| #24923623 | 2 |
| #24923618 | 2 |
| #24923614 | 2 |
| #24923264 | 2 |
| #24923262 | 2 |
| C4×C8×D167 | 2 |
| #488×C167 | 2 |
| #3131 | 167 |