Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×Dic334 | C2 | semidirect |
| 3. C2×#19128812 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic167 | C2 | semidirect |
| 6. C22×C4⋊C4×C167 | C2 | semidirect |
| 9. C22×Dic334 | C22 | semidirect |
| 14. #19128812 | C22 | direct (N × H) |
| 15. C2×C4⋊Dic167 | C22 | semidirect |
| 19. C2×C4⋊C4×C167 | C22 | semidirect |
| 22. C23×D167 | Q8 | semidirect |
| 25. C2×Dic334 | C23 | semidirect |
| 32. C4⋊Dic167 | C23 | semidirect |
| 39. C4⋊C4×C167 | C23 | semidirect |
| 43. C22×D167 | C2×Q8 | semidirect |
| 59. C22×C167 | C22⋊Q8 | semidirect |
| 67. C2×D167 | C22×Q8 | semidirect |
| 72. C2×C167 | C2×C22⋊Q8 | semidirect |
| 77. C167 | C22×C22⋊Q8 | semidirect |
| 83. C22×C4⋊C4 | D167 | semidirect |
| 96. C2×C4⋊C4 | C2×D167 | semidirect |
| 116. C4⋊C4 | C22×D167 | semidirect |
| 141. C22 | #19128812 | direct (N × H) |
| 151. C2 | C2×#19128812 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic334 | 2 |
| C23×C4×D167 | 2 |
| C2×#19128812 | 2 |
| C22×C4⋊Dic167 | 2 |
| C22×(C2×D167)⋊C4 | 2 |
| C22×C4⋊C4×C167 | 2 |
| C22×C22⋊Q8 | 167 |