Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2280 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 2280 conjugacy classes of subgroups — too many to draw. Only its 537 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×#3745 | C2 | semidirect |
| 2. C2×#64083 | C2 | semidirect |
| 3. C2×C32×C4×C8 | C2 | semidirect |
| 4. #10592394 | C2 | direct (N × H) |
| 11. C2×#3745 | C22 | semidirect |
| 13. #64083 | C22 | semidirect |
| 14. C32×C4×C8 | C22 | semidirect |
| 17. C2×C3×C4×C8 | D3 | semidirect |
| 27. C2×C32×C8 | D4 | semidirect |
| 41. C3×C4×C8 | C2×D3 | semidirect |
| 46. C2×C32×C4 | D8 | semidirect |
| 54. C32×C8 | C2×D4 | semidirect |
| 58. C2×C4×C8 | C3⋊D3 | semidirect |
| 67. C2×C3×C8 | D12 | semidirect |
| 79. C32×C4 | C2×D8 | semidirect |
| 89. C4×C8 | C2×C3⋊D3 | semidirect |
| 94. C2×C3×C4 | D24 | semidirect |
| 102. C3×C8 | C2×D12 | semidirect |
| 103. C2×C32 | #493 | semidirect |
| 116. C2×C8 | C4⋊(C3⋊D3) | semidirect |
| 127. C3×C4 | C2×D24 | semidirect |
| 129. C32 | C2×#493 | semidirect |
| 137. C2×C4 | #3745 | semidirect |
| 142. C8 | C2×C4⋊(C3⋊D3) | semidirect |
| 143. C2×C3 | #4695 | semidirect |
| 154. C4 | C2×#3745 | semidirect |
| 156. C3 | C2×#4695 | semidirect |
| 158. C2 | #10592394 | 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×#64083 | 2 |
| C2×C32×C4×C8 | 2 |
| #10592394 | 2 |
| C2×#4695 | 3 |