Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
841 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 841 conjugacy classes of subgroups — too many to draw. Only its 172 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 |
|---|---|---|
| 3. C2×#63574 | C2 | semidirect |
| 4. C3×#4551 | C2 | semidirect |
| 10. C2×C8×C3⋊D3 | C4 | semidirect |
| 20. #4551 | D3 | semidirect |
| 71. C3⋊(C3⋊C8) | C22⋊C4 | semidirect |
| 114. C2×C3⋊D3 | #106 | semidirect |
| 217. C32 | #1807 | semidirect |
| 262. C3 | #68868 | 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 |
| #10591325 | 2 |
| C2×#63574 | 2 |
| C3×#4551 | 2 |
| #68868 | 3 |