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. #24923173 | C2 | semidirect |
| 3. #24923160 | C2 | semidirect |
| 4. #24923158 | C2 | semidirect |
| 6. C4×(C2×D167)⋊C4 | C2 | semidirect |
| 7. #24923116 | C2 | semidirect |
| 8. #24923115 | C2 | semidirect |
| 9. #376×C167 | C2 | semidirect |
| 13. #19128820 | C4 | semidirect |
| 35. C2×Dic334 | C2×C4 | semidirect |
| 49. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 50. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 59. C42×C167 | C2×C4 | semidirect |
| 119. C167 | #2372 | semidirect |
| 129. #376 | D167 | semidirect |
| 179. C42 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128820 | 2 |
| #24923173 | 2 |
| #24923160 | 2 |
| #24923158 | 2 |
| #24923147 | 2 |
| C4×(C2×D167)⋊C4 | 2 |
| #24923116 | 2 |
| #24923115 | 2 |
| #376×C167 | 2 |
| #2372 | 167 |