Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128864 | C2 | semidirect |
| 2. C2×#19128861 | C2 | semidirect |
| 4. C4⋊Q8×D167 | C2 | semidirect |
| 5. #24923664 | C2 | semidirect |
| 6. #24923663 | C2 | semidirect |
| 7. #24923661 | C2 | semidirect |
| 8. #24923647 | C2 | semidirect |
| 9. #24923640 | C2 | semidirect |
| 10. #24923221 | C2 | semidirect |
| 11. #497×C167 | C2 | semidirect |
| 63. #14581933 | D4 | semidirect |
| 124. Dic167 | #137 | semidirect |
| 130. C167 | #3152 | semidirect |
| 139. #497 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128864 | 2 |
| C2×#19128861 | 2 |
| #24923818 | 2 |
| C4⋊Q8×D167 | 2 |
| #24923664 | 2 |
| #24923663 | 2 |
| #24923661 | 2 |
| #24923647 | 2 |
| #24923640 | 2 |
| #24923221 | 2 |
| #497×C167 | 2 |
| #3152 | 167 |