Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
762 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 168 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. #10593758 | C2 | semidirect |
| 3. C4⋊C4×#157 | C2 | semidirect |
| 6. #10593737 | C2 | semidirect |
| 7. C42×#157 | C2 | semidirect |
| 14. C32×#126 | C4 | semidirect |
| 15. #64107 | C4 | semidirect |
| 18. #64088 | C4 | semidirect |
| 19. #64085 | C4 | semidirect |
| 39. C32×C4⋊C4 | C2×C4 | semidirect |
| 41. C32×C42 | C2×C4 | semidirect |
| 45. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 46. #3750 | C2×C4 | semidirect |
| 47. #3750 | C2×C4 | semidirect |
| 48. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 109. #157 | #126 | direct (N × H) |
| 118. #126 | #157 | direct (N × H) |
| 161. C4⋊C4 | C2×#157 | semidirect |
| 171. C42 | C2×#157 | semidirect |
| 183. C32 | C4×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#126 | 2 |
| #10593758 | 2 |
| C4⋊C4×#157 | 2 |
| #10593747 | 2 |
| C22⋊C4×#157 | 2 |
| #10593737 | 2 |
| C42×#157 | 2 |
| C4×#126 | 9 |