Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19128858 | C2 | semidirect |
| 2. #24923819 | C2 | semidirect |
| 3. #24923656 | C2 | semidirect |
| 4. #24923645 | C2 | semidirect |
| 5. #24923641 | C2 | semidirect |
| 6. C4×#14581934 | C2 | semidirect |
| 7. C2×#127×C167 | C2 | semidirect |
| 10. C2×#14581938 | C22 | semidirect |
| 11. C2×#14581935 | C22 | semidirect |
| 13. #19128832 | C22 | semidirect |
| 14. #19128829 | C22 | semidirect |
| 15. #19128820 | C22 | semidirect |
| 18. #19128743 | C22 | semidirect |
| 19. C4×C167⋊C8 | C22 | semidirect |
| 34. #14581934 | D4 | semidirect |
| 57. C167⋊C8 | C2×D4 | semidirect |
| 82. C4×C167 | AGL(1,ℤ/8) | semidirect |
| 90. C167 | #3151 | semidirect |
| 94. C2×#127 | D167 | semidirect |
| 174. C4 | #19128858 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128858 | 2 |
| #24923819 | 2 |
| #24923656 | 2 |
| #24923645 | 2 |
| #24923641 | 2 |
| C4×#14581934 | 2 |
| C2×#127×C167 | 2 |
| #3151 | 167 |