Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
588 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 177 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. C8×C4⋊(C3⋊D3) | C2 | semidirect |
| 3. C32×C82 | C2 | semidirect |
| 4. #10589325 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 19. C3×C82 | D3 | semidirect |
| 33. #3745 | C8 | direct (N × H) |
| 52. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 58. C32×C8 | C2×C8 | semidirect |
| 59. C32×C8 | D8 | semidirect |
| 65. C82 | C3⋊D3 | semidirect |
| 111. C3×C8 | D3×C8 | semidirect |
| 112. C3×C8 | D24 | semidirect |
| 141. C32 | C8×D8 | semidirect |
| 155. C8 | C8×C3⋊D3 | semidirect |
| 156. C8 | #3745 | direct (N × H) |
| 171. C3 | C8×D24 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3745 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| C32×C82 | 2 |
| #10589325 | 2 |
| #10589324 | 2 |
| C8×D24 | 3 |