Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
489 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10593625 | C2 | semidirect |
| 3. C3×#5391 | C2 | semidirect |
| 5. #10593202 | C2 | semidirect |
| 21. #5391 | D3 | direct (N × H) |
| 34. D3×SL(2,𝔽3) | Q8 | semidirect |
| 80. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 196. SL(2,𝔽3) | D3×Q8 | semidirect |
| 289. D3 | #5391 | direct (N × H) |
| 305. C3 | C2×#5391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D3×SL(2,𝔽3) | 2 |
| #10593625 | 2 |
| C3×#5391 | 2 |
| D3×#859 | 2 |
| #10593202 | 2 |
| C2×#5391 | 3 |
| D3×#477 | 3 |
| D3×C4⋊Dic3 | 4 |