Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×Dic668 | C2 | semidirect |
| 4. #24923528 | C2 | direct (N × H) |
| 5. C2×#19128755 | C2 | semidirect |
| 6. C2×#106×C167 | C2 | semidirect |
| 10. C2×Dic668 | C22 | semidirect |
| 18. #19128755 | C22 | semidirect |
| 21. #106×C167 | C22 | semidirect |
| 79. C2×C167 | #470 | semidirect |
| 83. C167 | C2×#470 | semidirect |
| 89. C2×#106 | D167 | semidirect |
| 104. #106 | C2×D167 | semidirect |
| 164. C2 | #24923528 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic668 | 2 |
| C22×#14581933 | 2 |
| C2×#19128812 | 2 |
| #24923528 | 2 |
| C2×#19128755 | 2 |
| C2×#106×C167 | 2 |
| C2×#470 | 167 |