Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
296 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 1. C3×Q8×SL(2,𝔽3) | C2 | semidirect |
| 3. C3×C8×SL(2,𝔽3) | C2 | semidirect |
| 4. C3×#3362 | C3 | semidirect |
| 5. #3362⋊C3 | C3 | direct (N × H) |
| 12. Q8×SL(2,𝔽3) | C2×C3 | semidirect |
| 19. C8×SL(2,𝔽3) | C2×C3 | semidirect |
| 25. #3362 | C32 | semidirect |
| 51. C3×SL(2,𝔽3) | SD16 | semidirect |
| 113. C3×Q8 | #41⋊C3 | semidirect |
| 130. SL(2,𝔽3) | C3×SD16 | semidirect |
| 180. Q8 | C3×#41⋊C3 | semidirect |
| 216. C3 | #3362⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×SL(2,𝔽3) | 2 |
| C3×C4⋊(#41⋊C3) | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| C3×#3362 | 3 |
| #3362⋊C3 | 3 |
| C32×#103 | 4 |