Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
241 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 52 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. C3×SL(2,𝔽3)⋊C8 | C2 | semidirect |
| 3. #73069 | C3 | direct (N × H) |
| 14. SL(2,𝔽3)⋊C8 | C2×C3 | semidirect |
| 197. C3 | #73069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×#41⋊C3 | 2 |
| C3×SL(2,𝔽3)⋊C8 | 2 |
| #73069 | 3 |
| C3×#1488 | 3 |
| C3×#803 | 4 |