Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
754 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 754 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 |
|---|---|---|
| 2. C2×#19128861 | C2 | semidirect |
| 3. C22⋊Q8×D167 | C2 | semidirect |
| 4. #24923432 | C2 | semidirect |
| 5. #24923428 | C2 | semidirect |
| 6. #24923427 | C2 | semidirect |
| 7. #24923424 | C2 | semidirect |
| 8. #24923420 | C2 | semidirect |
| 9. #24923267 | C2 | semidirect |
| 10. #24923231 | C2 | semidirect |
| 11. #450×C167 | C2 | semidirect |
| 18. C2×Q8×D167 | C22 | semidirect |
| 23. C2×Dic668 | C22 | semidirect |
| 24. C2×#14581940 | C22 | semidirect |
| 25. C2×#14581938 | C22 | semidirect |
| 26. C2×#14581933 | C22 | semidirect |
| 27. #19128812 | C22 | semidirect |
| 31. #19128808 | C22 | semidirect |
| 33. C4⋊C4×D167 | C22 | semidirect |
| 35. #19128757 | C22 | semidirect |
| 36. #19128755 | C22 | semidirect |
| 37. #19128753 | C22 | semidirect |
| 39. (C2×D167)⋊C8 | C22 | semidirect |
| 41. C2×SD16×C167 | C22 | semidirect |
| 43. #102×C167 | C22 | semidirect |
| 146. C22×C167 | #137 | semidirect |
| 171. C167 | #3007 | semidirect |
| 181. #450 | D167 | semidirect |
| 199. C2×SD16 | C2×D167 | semidirect |
| 213. #102 | C2×D167 | semidirect |
| 325. C22 | #19128861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581949 | 2 |
| C2×#19128861 | 2 |
| C22⋊Q8×D167 | 2 |
| #24923432 | 2 |
| #24923428 | 2 |
| #24923427 | 2 |
| #24923424 | 2 |
| #24923420 | 2 |
| #24923267 | 2 |
| #24923231 | 2 |
| #450×C167 | 2 |
| #3007 | 167 |