Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14581951 | C2 | semidirect |
| 2. C2×#19128853 | C2 | semidirect |
| 3. #24923779 | C2 | semidirect |
| 4. #24923434 | C2 | semidirect |
| 5. #24923425 | C2 | semidirect |
| 6. #24923422 | C2 | semidirect |
| 7. #24923413 | C2 | semidirect |
| 8. #24923402 | C2 | semidirect |
| 9. #24923264 | C2 | semidirect |
| 10. C22⋊C8×D167 | C2 | semidirect |
| 11. #448×C167 | C2 | semidirect |
| 17. C2×#14581949 | C22 | semidirect |
| 23. C2×#14581940 | C22 | semidirect |
| 24. C2×#14581939 | C22 | semidirect |
| 25. C2×#14581935 | C22 | semidirect |
| 26. C2×C8×D167 | C22 | semidirect |
| 28. #19128812 | C22 | semidirect |
| 30. #19128803 | C22 | semidirect |
| 34. #19128790 | C22 | semidirect |
| 35. #19128756 | C22 | semidirect |
| 36. #19128754 | C22 | semidirect |
| 37. #19128752 | C22 | semidirect |
| 39. (C2×D167)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C167 | C22 | semidirect |
| 43. #103×C167 | C22 | semidirect |
| 52. #14581951 | D4 | semidirect |
| 146. C22×C167 | #135 | semidirect |
| 175. C167 | #3002 | semidirect |
| 184. #448 | D167 | semidirect |
| 202. C2×SD16 | C2×D167 | semidirect |
| 215. #103 | C2×D167 | semidirect |
| 333. C22 | #19128853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581951 | 2 |
| C2×#19128853 | 2 |
| #24923779 | 2 |
| #24923434 | 2 |
| #24923425 | 2 |
| #24923422 | 2 |
| #24923413 | 2 |
| #24923402 | 2 |
| #24923264 | 2 |
| C22⋊C8×D167 | 2 |
| #448×C167 | 2 |
| #3002 | 167 |