Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
672 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 169 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. C32×#492 | C2 | semidirect |
| 2. #10592787 | C2 | semidirect |
| 3. #10592777 | C2 | semidirect |
| 5. #10592769 | C2 | semidirect |
| 6. #10592392 | C2 | semidirect |
| 7. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 22. C3×#492 | D3 | semidirect |
| 77. C32×C8 | D8 | semidirect |
| 79. C3⋊(C3⋊C8) | SD16 | semidirect |
| 83. #492 | C3⋊D3 | semidirect |
| 146. C3×C8 | #213 | semidirect |
| 185. C32 | #1706 | semidirect |
| 203. C8 | #3753 | semidirect |
| 221. C3 | #71255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| #10592787 | 2 |
| #10592777 | 2 |
| #10592772 | 2 |
| #10592769 | 2 |
| #10592392 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71255 | 3 |