Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19128856 | C2 | semidirect |
| 2. #24923817 | C2 | semidirect |
| 3. #127×D167 | C2 | semidirect |
| 4. #24923657 | C2 | semidirect |
| 5. #24923645 | C2 | semidirect |
| 6. #24923642 | C2 | semidirect |
| 7. #24923641 | C2 | semidirect |
| 8. C4×#14581933 | C2 | semidirect |
| 9. #493×C167 | C2 | semidirect |
| 14. C2×#14581939 | C22 | semidirect |
| 15. C2×#14581938 | C22 | semidirect |
| 16. C2×#14581935 | C22 | semidirect |
| 18. #19128832 | C22 | semidirect |
| 22. #19128819 | C22 | semidirect |
| 26. #19128742 | C22 | semidirect |
| 27. C4×C167⋊C8 | C22 | semidirect |
| 28. C2×D8×C167 | C22 | semidirect |
| 30. #127×C167 | C22 | semidirect |
| 31. C4×C8×C167 | C22 | semidirect |
| 48. #14581933 | D4 | semidirect |
| 77. C167⋊C8 | C2×D4 | semidirect |
| 86. C8×C167 | C2×D4 | semidirect |
| 97. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 108. C167 | #3151 | semidirect |
| 115. #493 | D167 | semidirect |
| 126. C2×D8 | C2×D167 | semidirect |
| 133. #127 | C2×D167 | semidirect |
| 140. C4×C8 | C2×D167 | semidirect |
| 195. C8 | D4×D167 | semidirect |
| 209. C4 | #19128856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128856 | 2 |
| #24923817 | 2 |
| #127×D167 | 2 |
| #24923657 | 2 |
| #24923645 | 2 |
| #24923642 | 2 |
| #24923641 | 2 |
| C4×#14581933 | 2 |
| #493×C167 | 2 |
| #3151 | 167 |