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×#19128864 | C2 | semidirect |
| 3. C22⋊Q8×D167 | C2 | semidirect |
| 4. #24923434 | C2 | semidirect |
| 5. #24923430 | C2 | semidirect |
| 6. #24923425 | C2 | semidirect |
| 7. #24923422 | C2 | semidirect |
| 8. #24923419 | C2 | semidirect |
| 9. #24923269 | C2 | semidirect |
| 10. #24923231 | C2 | semidirect |
| 11. #451×C167 | C2 | semidirect |
| 17. C2×Q8×D167 | C22 | semidirect |
| 23. C2×#14581940 | C22 | semidirect |
| 24. C2×#14581939 | C22 | semidirect |
| 25. C2×#14581937 | C22 | semidirect |
| 26. C2×#14581933 | C22 | semidirect |
| 27. #19128812 | C22 | semidirect |
| 31. #19128808 | C22 | semidirect |
| 33. C4⋊C4×D167 | C22 | semidirect |
| 35. #19128756 | C22 | semidirect |
| 36. #19128754 | C22 | semidirect |
| 37. #19128752 | C22 | semidirect |
| 39. (C2×D167)⋊C8 | C22 | semidirect |
| 41. C2×Q16×C167 | C22 | semidirect |
| 43. #103×C167 | C22 | semidirect |
| 142. C22×C167 | #137 | semidirect |
| 171. C167 | #3007 | semidirect |
| 179. #451 | D167 | semidirect |
| 197. C2×Q16 | C2×D167 | semidirect |
| 211. #103 | C2×D167 | semidirect |
| 325. C22 | #19128864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581951 | 2 |
| C2×#19128864 | 2 |
| C22⋊Q8×D167 | 2 |
| #24923434 | 2 |
| #24923430 | 2 |
| #24923425 | 2 |
| #24923422 | 2 |
| #24923419 | 2 |
| #24923269 | 2 |
| #24923231 | 2 |
| #451×C167 | 2 |
| #3007 | 167 |