Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
601 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 601 conjugacy classes of subgroups — too many to draw. Only its 119 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. #5570⋊C3 | C2 | direct (N × H) |
| 4. C2×#5570 | C3 | semidirect |
| 13. #5570 | C2×C3 | semidirect |
| 23. C2×C3×SL(2,𝔽3) | Q8 | semidirect |
| 57. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 81. C2×SL(2,𝔽3) | Dic6 | semidirect |
| 147. SL(2,𝔽3) | C2×Dic6 | semidirect |
| 223. C2×C3 | #557⋊C3 | semidirect |
| 240. C3 | C2×#557⋊C3 | semidirect |
| 241. C2 | #5570⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×SL(2,𝔽3) | 2 |
| C2×Dic3×SL(2,𝔽3) | 2 |
| #5570⋊C3 | 2 |
| C2×#5570 | 3 |
| C2×#557⋊C3 | 3 |
| C2×C3×C4⋊Dic3 | 4 |