Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
652 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 249 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×Q8×Dic167 | C2 | semidirect |
| 3. #24923176 | C2 | semidirect |
| 5. #24923162 | C2 | semidirect |
| 6. #24923135 | C2 | semidirect |
| 7. C22⋊C4×Dic167 | C2 | semidirect |
| 8. C42×Dic167 | C2 | semidirect |
| 27. #124×C167 | C4 | semidirect |
| 50. C2×Q8×C167 | C2×C4 | semidirect |
| 57. C22⋊C4×C167 | C2×C4 | semidirect |
| 58. C42×C167 | C2×C4 | semidirect |
| 105. Dic167 | #124 | direct (N × H) |
| 112. C167 | C4×#124 | semidirect |
| 126. #124 | Dic167 | direct (N × H) |
| 146. C2×Q8 | C2×Dic167 | semidirect |
| 165. C22⋊C4 | C2×Dic167 | semidirect |
| 171. C42 | C2×Dic167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic167 | 2 |
| C2×D4×Dic167 | 2 |
| #24923176 | 2 |
| #24923172 | 2 |
| #24923162 | 2 |
| #24923135 | 2 |
| C22⋊C4×Dic167 | 2 |
| C42×Dic167 | 2 |
| C2×#124×C167 | 2 |
| C4×#124 | 167 |