Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D167 | C2 | semidirect |
| 2. C2×#19128864 | C2 | semidirect |
| 4. #24923424 | C2 | semidirect |
| 5. #24923423 | C2 | semidirect |
| 6. #24923410 | C2 | semidirect |
| 7. #24923409 | C2 | semidirect |
| 8. #24923408 | C2 | semidirect |
| 9. #24923276 | C2 | semidirect |
| 10. #24923231 | C2 | semidirect |
| 11. #451×C167 | C2 | semidirect |
| 23. C2×#14581940 | C22 | semidirect |
| 24. C2×#14581939 | C22 | semidirect |
| 25. C2×#14581937 | C22 | semidirect |
| 35. #19128757 | C22 | semidirect |
| 36. #19128756 | C22 | semidirect |
| 37. #19128755 | C22 | semidirect |
| 41. C2×Q16×C167 | C22 | semidirect |
| 43. #103×C167 | C22 | semidirect |
| 58. Q8×D167 | D4 | semidirect |
| 141. C22×C167 | #137 | semidirect |
| 152. C2×D167 | #137 | semidirect |
| 169. C167 | #3004 | semidirect |
| 176. #451 | D167 | semidirect |
| 195. C2×Q16 | C2×D167 | semidirect |
| 211. #103 | C2×D167 | semidirect |
| 321. C22 | #19128864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D167 | 2 |
| C2×#19128864 | 2 |
| #24923782 | 2 |
| #24923424 | 2 |
| #24923423 | 2 |
| #24923410 | 2 |
| #24923409 | 2 |
| #24923408 | 2 |
| #24923276 | 2 |
| #24923231 | 2 |
| #451×C167 | 2 |
| #3004 | 167 |