Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19128863 | C2 | semidirect |
| 2. C2×M16×D167 | C2 | semidirect |
| 4. C2×#19128808 | C2 | semidirect |
| 5. #24923526 | C2 | semidirect |
| 6. #24923518 | C2 | semidirect |
| 7. #24923509 | C2 | semidirect |
| 8. #24923501 | C2 | semidirect |
| 9. #24923312 | C2 | semidirect |
| 10. #24923271 | C2 | semidirect |
| 11. #419×C167 | C2 | semidirect |
| 15. C2×#14581940 | C22 | semidirect |
| 16. C2×#14581937 | C22 | semidirect |
| 36. #19128765 | C22 | semidirect |
| 37. #19128763 | C22 | semidirect |
| 38. #19128757 | C22 | semidirect |
| 39. #19128754 | C22 | semidirect |
| 43. #103×C167 | C22 | semidirect |
| 44. #103×C167 | C22 | semidirect |
| 64. #14581934 | D4 | semidirect |
| 145. C2×D167 | #137 | semidirect |
| 163. C167 | #3056 | semidirect |
| 174. #419 | D167 | semidirect |
| 206. #103 | C2×D167 | semidirect |
| 207. #103 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128863 | 2 |
| C2×M16×D167 | 2 |
| #24923781 | 2 |
| C2×#19128808 | 2 |
| #24923526 | 2 |
| #24923518 | 2 |
| #24923509 | 2 |
| #24923501 | 2 |
| #24923312 | 2 |
| #24923271 | 2 |
| #419×C167 | 2 |
| #3056 | 167 |