Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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. #24923826 | C2 | semidirect |
| 3. #24923678 | C2 | semidirect |
| 4. #24923663 | C2 | semidirect |
| 5. #24923638 | C2 | semidirect |
| 6. #24923629 | C2 | semidirect |
| 7. #24923527 | C2 | semidirect |
| 9. C4×Dic668 | C2 | semidirect |
| 10. C4×#14581939 | C2 | semidirect |
| 11. C4×M16×C167 | C2 | semidirect |
| 129. C167 | #3172 | semidirect |
| 141. C4×M16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923826 | 2 |
| #24923803 | 2 |
| #24923678 | 2 |
| #24923663 | 2 |
| #24923638 | 2 |
| #24923629 | 2 |
| #24923527 | 2 |
| #24923515 | 2 |
| C4×Dic668 | 2 |
| C4×#14581939 | 2 |
| C4×M16×C167 | 2 |
| #3172 | 167 |