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×#19128859 | C2 | semidirect |
| 2. #24923941 | C2 | semidirect |
| 3. #24923904 | C2 | semidirect |
| 4. #24923645 | C2 | semidirect |
| 5. #24923521 | C2 | semidirect |
| 6. #24923465 | C2 | semidirect |
| 7. #24923413 | C2 | semidirect |
| 8. #24923404 | C2 | semidirect |
| 9. C4×#14581937 | C2 | semidirect |
| 10. #24923346 | C2 | semidirect |
| 11. #460×C167 | C2 | semidirect |
| 12. C2×#14581951 | C22 | semidirect |
| 18. C2×#14581935 | C22 | semidirect |
| 19. C2×#14581935 | C22 | semidirect |
| 20. C2×#14581933 | C22 | semidirect |
| 22. #19128829 | C22 | semidirect |
| 24. #19128807 | C22 | semidirect |
| 31. #19128763 | C22 | semidirect |
| 32. #19128756 | C22 | semidirect |
| 33. #19128754 | C22 | semidirect |
| 35. (C2×D167)⋊C8 | C22 | semidirect |
| 36. C4×C167⋊C8 | C22 | semidirect |
| 37. C2×SD16×C167 | C22 | semidirect |
| 39. C4×Q8×C167 | C22 | semidirect |
| 40. C4⋊C8×C167 | C22 | semidirect |
| 41. #102×C167 | C22 | semidirect |
| 60. #14581937 | D4 | semidirect |
| 107. C167⋊C8 | C2×D4 | semidirect |
| 110. Q8×C167 | C2×D4 | semidirect |
| 138. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 150. C167 | #3274 | semidirect |
| 157. #460 | D167 | semidirect |
| 168. C2×SD16 | C2×D167 | semidirect |
| 181. C4×Q8 | C2×D167 | semidirect |
| 186. C4⋊C8 | C2×D167 | semidirect |
| 190. #102 | C2×D167 | semidirect |
| 242. Q8 | D4×D167 | semidirect |
| 291. C4 | #19128859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128859 | 2 |
| #24923941 | 2 |
| #24923904 | 2 |
| #24923645 | 2 |
| #24923521 | 2 |
| #24923465 | 2 |
| #24923413 | 2 |
| #24923404 | 2 |
| C4×#14581937 | 2 |
| #24923346 | 2 |
| #460×C167 | 2 |
| #3274 | 167 |