Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
841 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 841 conjugacy classes of subgroups — too many to draw. Only its 196 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. C2×C3×#817 | C2 | semidirect |
| 4. #10589163 | C2 | semidirect |
| 10. C2×C8×C3⋊D3 | C4 | semidirect |
| 18. C2×#817 | D3 | semidirect |
| 72. C32×C8 | C22⋊C4 | semidirect |
| 120. C2×C3⋊D3 | #106 | semidirect |
| 175. C3×C8 | (C2×D3)⋊C4 | semidirect |
| 228. C32 | #1807 | semidirect |
| 247. C8 | #3722 | semidirect |
| 273. C3 | #70577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×C3⋊D3 | 2 |
| C2×C3×#817 | 2 |
| #10591325 | 2 |
| #10589163 | 2 |
| #70577 | 3 |