Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1860 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1860 conjugacy classes of subgroups — too many to draw. Only its 233 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×C32×#100 | C2 | semidirect |
| 3. #10592920 | C2 | semidirect |
| 4. C2×#63652 | C2 | semidirect |
| 5. #10592832 | C2 | semidirect |
| 11. #64361 | C4 | semidirect |
| 15. C2×C32×M16 | C22 | semidirect |
| 17. C2×C4⋊(C3⋊Dic3) | C22 | semidirect |
| 18. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 24. C2×C3×#100 | D3 | semidirect |
| 68. C2×C3×M16 | C2×D3 | semidirect |
| 103. C4⋊(C3⋊D3) | C22⋊C4 | semidirect |
| 107. #634 | C22⋊C4 | semidirect |
| 112. C2×#100 | C3⋊D3 | semidirect |
| 172. C2×M16 | C2×C3⋊D3 | semidirect |
| 270. C32 | #1792 | semidirect |
| 330. C3 | #70086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64361 | 2 |
| C2×C32×#100 | 2 |
| #10592920 | 2 |
| C2×#63652 | 2 |
| #10592832 | 2 |
| #70086 | 3 |