Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
410 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. #10590169 | C2 | semidirect |
| 23. #3787 | C8 | semidirect |
| 48. #622 | C2×C8 | semidirect |
| 101. C3⋊D3 | #322 | semidirect |
| 126. C32 | C2×#322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3787 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #10590169 | 2 |
| C2×#322 | 9 |