Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923939 | C2 | semidirect |
| 3. #24923904 | C2 | semidirect |
| 4. #24923519 | C2 | semidirect |
| 5. #24923466 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923411 | C2 | semidirect |
| 8. #24923401 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. #24923348 | C2 | semidirect |
| 11. #493×C167 | C2 | semidirect |
| 12. C2×#14581949 | C22 | semidirect |
| 17. C2×#14581938 | C22 | semidirect |
| 19. C2×#14581933 | C22 | semidirect |
| 24. #19128803 | C22 | semidirect |
| 26. C4×Dic334 | C22 | semidirect |
| 30. #19128764 | C22 | semidirect |
| 31. C4⋊(C167⋊C8) | C22 | semidirect |
| 32. #19128757 | C22 | semidirect |
| 34. #19128753 | C22 | semidirect |
| 35. #19128753 | C22 | semidirect |
| 36. (C2×D167)⋊C8 | C22 | semidirect |
| 37. C2×D8×C167 | C22 | semidirect |
| 38. C2×D8×C167 | C22 | semidirect |
| 40. #127×C167 | C22 | semidirect |
| 41. C4×C8×C167 | C22 | semidirect |
| 58. #14581939 | D4 | semidirect |
| 89. Dic334 | C2×D4 | semidirect |
| 120. C8×C167 | C2×D4 | semidirect |
| 136. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 150. C167 | #3274 | semidirect |
| 155. #493 | D167 | semidirect |
| 170. C2×D8 | C2×D167 | semidirect |
| 171. C2×D8 | C2×D167 | semidirect |
| 175. #127 | C2×D167 | semidirect |
| 192. C4×C8 | C2×D167 | semidirect |
| 271. C8 | D4×D167 | semidirect |
| 291. 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 |
| #24923939 | 2 |
| #24923904 | 2 |
| #24923519 | 2 |
| #24923466 | 2 |
| #24923461 | 2 |
| #24923411 | 2 |
| #24923401 | 2 |
| C4×#14581939 | 2 |
| #24923348 | 2 |
| #493×C167 | 2 |
| #3274 | 167 |