Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
560 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #24923176 | C2 | semidirect |
| 3. #24923161 | C2 | semidirect |
| 4. #24923159 | C2 | semidirect |
| 6. C4×(C2×D167)⋊C4 | C2 | semidirect |
| 7. #24923116 | C2 | semidirect |
| 8. #24923114 | C2 | semidirect |
| 9. #391×C167 | C2 | semidirect |
| 12. #19128821 | C4 | semidirect |
| 46. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 47. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic167 | C2×C4 | semidirect |
| 54. C2×Q8×C167 | C2×C4 | semidirect |
| 123. C167 | #2372 | semidirect |
| 127. #391 | D167 | semidirect |
| 159. C2×Q8 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128821 | 2 |
| #24923176 | 2 |
| #24923161 | 2 |
| #24923159 | 2 |
| #24923147 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| #24923116 | 2 |
| #24923114 | 2 |
| #391×C167 | 2 |
| #2372 | 167 |