Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1968 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 1968 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×#3744 | C2 | semidirect |
| 3. C2×#64078 | C2 | semidirect |
| 4. C2×C32×C4×C8 | C2 | semidirect |
| 5. #10592392 | C2 | direct (N × H) |
| 14. C2×#3744 | C22 | semidirect |
| 18. #64078 | C22 | semidirect |
| 19. C32×C4×C8 | C22 | semidirect |
| 23. C2×C3×C4×C8 | D3 | semidirect |
| 37. C2×C32×C8 | D4 | semidirect |
| 56. C3×C4×C8 | C2×D3 | semidirect |
| 61. C2×C32×C4 | SD16 | semidirect |
| 73. C32×C8 | C2×D4 | semidirect |
| 78. C2×C4×C8 | C3⋊D3 | semidirect |
| 91. C2×C3×C8 | D12 | semidirect |
| 104. C32×C4 | C2×SD16 | semidirect |
| 119. C4×C8 | C2×C3⋊D3 | semidirect |
| 124. C2×C3×C4 | #204 | semidirect |
| 136. C3×C8 | C2×D12 | semidirect |
| 137. C2×C32 | #492 | semidirect |
| 154. C2×C8 | C4⋊(C3⋊D3) | semidirect |
| 166. C3×C4 | C2×#204 | semidirect |
| 169. C32 | C2×#492 | semidirect |
| 181. C2×C4 | #3744 | semidirect |
| 186. C8 | C2×C4⋊(C3⋊D3) | semidirect |
| 187. C2×C3 | #4693 | semidirect |
| 199. C4 | C2×#3744 | semidirect |
| 201. C3 | C2×#4693 | semidirect |
| 203. C2 | #10592392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3744 | 2 |
| C2×#64083 | 2 |
| C2×#64078 | 2 |
| C2×C32×C4×C8 | 2 |
| #10592392 | 2 |
| C2×#4693 | 3 |