Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 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. #24923172 | C2 | semidirect |
| 3. #24923169 | C2 | semidirect |
| 4. #24923163 | C2 | semidirect |
| 5. #24923161 | C2 | semidirect |
| 6. #24923158 | C2 | semidirect |
| 7. #24923148 | C2 | semidirect |
| 8. #24923124 | C2 | semidirect |
| 9. #386×C167 | C2 | semidirect |
| 12. #19128800 | C4 | semidirect |
| 13. C2×C4⋊Dic167 | C22 | semidirect |
| 14. C2×Dic167⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic167 | C22 | semidirect |
| 23. C2×C4×Dic167 | C22 | semidirect |
| 24. C2×C4×Dic167 | C22 | semidirect |
| 25. C167⋊#95 | C22 | semidirect |
| 26. C167⋊#95 | C22 | semidirect |
| 28. C23×C4×C167 | C22 | semidirect |
| 30. C2×C22⋊C4×C167 | C22 | semidirect |
| 31. #95×C167 | C22 | semidirect |
| 36. C23×D167 | C2×C4 | semidirect |
| 48. C22⋊Dic167 | C2×C4 | semidirect |
| 53. (C2×D167)⋊C4 | C2×C4 | semidirect |
| 149. C167 | #2375 | semidirect |
| 158. #386 | D167 | semidirect |
| 163. C23×C4 | C2×D167 | semidirect |
| 176. C2×C22⋊C4 | C2×D167 | semidirect |
| 181. #95 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128800 | 2 |
| #24923172 | 2 |
| #24923169 | 2 |
| #24923163 | 2 |
| #24923161 | 2 |
| #24923158 | 2 |
| #24923148 | 2 |
| #24923124 | 2 |
| #386×C167 | 2 |
| #2375 | 167 |