Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. M16×Dic167 | C2 | semidirect |
| 5. #24923115 | C2 | semidirect |
| 6. #24923028 | C2 | semidirect |
| 7. #339×C167 | C2 | semidirect |
| 10. #19128797 | C4 | semidirect |
| 11. #19128794 | C4 | semidirect |
| 17. #19128760 | C4 | semidirect |
| 18. #19128758 | C4 | semidirect |
| 37. #14581934 | C2×C4 | semidirect |
| 44. C4×Dic167 | C2×C4 | semidirect |
| 50. M16×C167 | C2×C4 | semidirect |
| 56. C42×C167 | C2×C4 | semidirect |
| 106. C167 | #1759 | semidirect |
| 114. #339 | D167 | semidirect |
| 148. M16 | C4×D167 | semidirect |
| 163. C42 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923737 | 2 |
| C2×#19128760 | 2 |
| C2×#19128758 | 2 |
| M16×Dic167 | 2 |
| #24923115 | 2 |
| #24923028 | 2 |
| #339×C167 | 2 |
| #1759 | 167 |