Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1824 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 1824 conjugacy classes of subgroups — too many to draw. Only its 393 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×#64102 | C2 | semidirect |
| 3. C2×C32×#106 | C2 | semidirect |
| 4. C2×#63642 | C2 | semidirect |
| 5. C2×#63636 | C2 | semidirect |
| 6. #10592568 | C2 | direct (N × H) |
| 15. C2×#3745 | C4 | semidirect |
| 18. #64102 | C22 | semidirect |
| 19. C32×#106 | C22 | semidirect |
| 20. #63642 | C22 | semidirect |
| 21. #63636 | C22 | semidirect |
| 24. C2×C3×#106 | D3 | semidirect |
| 34. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 38. C2×C32×C8 | C2×C4 | semidirect |
| 47. #3745 | C2×C4 | semidirect |
| 60. C3×#106 | C2×D3 | semidirect |
| 78. C4⋊(C3⋊D3) | C22×C4 | semidirect |
| 80. C32×C8 | C22×C4 | semidirect |
| 85. C2×#106 | C3⋊D3 | semidirect |
| 98. C2×C3×C8 | C4×D3 | semidirect |
| 131. #106 | C2×C3⋊D3 | semidirect |
| 151. C3×C8 | C2×C4×D3 | semidirect |
| 153. C2×C32 | #442 | semidirect |
| 170. C2×C8 | C4×C3⋊D3 | semidirect |
| 189. C32 | C2×#442 | semidirect |
| 208. C8 | C2×C4×C3⋊D3 | semidirect |
| 209. C2×C3 | #4869 | semidirect |
| 225. C3 | C2×#4869 | semidirect |
| 227. C2 | #10592568 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C2×#64102 | 2 |
| C2×C32×#106 | 2 |
| C2×#63642 | 2 |
| C2×#63636 | 2 |
| #10592568 | 2 |
| C2×#4869 | 3 |