Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
326 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10593749 | C2 | semidirect |
| 3. #10590170 | C2 | semidirect |
| 4. #10590168 | C2 | semidirect |
| 5. #10590160 | C2 | semidirect |
| 28. #3745 | C8 | semidirect |
| 41. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 47. C32×C8 | C2×C8 | semidirect |
| 117. C32 | #1580 | semidirect |
| 131. C8 | #3787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593749 | 2 |
| #10592571 | 2 |
| #10590170 | 2 |
| #10590168 | 2 |
| #10590160 | 2 |
| #1580 | 9 |