Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1968 conjugacy classes of subgroups; only the 457 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 457 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. C2×C32×C4⋊Q8 | C2 | semidirect |
| 2. C22×#3755 | C2 | semidirect |
| 4. #10592784 | C2 | direct (N × H) |
| 5. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 11. C32×C4⋊Q8 | C22 | semidirect |
| 15. C2×#3755 | C22 | semidirect |
| 19. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C2×C3×C4⋊Q8 | D3 | semidirect |
| 41. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 48. C3×C4⋊Q8 | C2×D3 | semidirect |
| 65. C2×C32×C4 | SD16 | semidirect |
| 73. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 75. C2×C4⋊Q8 | C3⋊D3 | semidirect |
| 105. C32×C4 | C2×SD16 | semidirect |
| 114. C4⋊Q8 | C2×C3⋊D3 | semidirect |
| 128. C2×C3×C4 | #215 | semidirect |
| 137. C2×C32 | #492 | semidirect |
| 167. C3×C4 | C2×#215 | semidirect |
| 169. C32 | C2×#492 | semidirect |
| 181. C2×C4 | #3755 | semidirect |
| 187. C2×C3 | #5085 | semidirect |
| 199. C4 | C2×#3755 | semidirect |
| 201. C3 | C2×#5085 | semidirect |
| 203. C2 | #10592784 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊Q8 | 2 |
| C22×#3755 | 2 |
| C2×#64083 | 2 |
| #10592784 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#5085 | 3 |