Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
505 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 505 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #10593202 | C2 | direct (N × H) |
| 29. C2×C3×SL(2,𝔽3) | Q8 | semidirect |
| 67. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 94. C2×SL(2,𝔽3) | Dic6 | semidirect |
| 166. SL(2,𝔽3) | C2×Dic6 | semidirect |
| 249. C2×C3 | #5391 | semidirect |
| 266. C3 | C2×#5391 | semidirect |
| 267. C2 | #10593202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic3×SL(2,𝔽3) | 2 |
| C2×C3⋊#859 | 2 |
| C2×C3×#859 | 2 |
| #10593202 | 2 |
| C2×#5391 | 3 |
| C2×#4793 | 3 |
| C2×Dic3⋊Dic3 | 4 |