Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
644 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
| 2. C3×#557⋊C3 | C2 | semidirect |
| 4. C3×Q8×#41 | C3 | semidirect |
| 5. Q8×#41⋊C3 | C3 | direct (N × H) |
| 17. Q8×SL(2,𝔽3) | C2×C3 | semidirect |
| 18. #557⋊C3 | C2×C3 | semidirect |
| 21. C3×#41⋊C3 | Q8 | direct (N × H) |
| 25. Q8×#41 | C32 | semidirect |
| 53. C3×SL(2,𝔽3) | C2×Q8 | semidirect |
| 62. C3×#41 | C3×Q8 | semidirect |
| 73. #41⋊C3 | C3×Q8 | direct (N × H) |
| 116. C3×Q8 | #41⋊C3 | direct (N × H) |
| 133. SL(2,𝔽3) | C2×C3×Q8 | semidirect |
| 138. #41 | C32×Q8 | semidirect |
| 179. Q8 | C3×#41⋊C3 | direct (N × H) |
| 212. C3 | Q8×#41⋊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×#557⋊C3 | 2 |
| C3×C4×#41⋊C3 | 2 |
| C3×Q8×#41 | 3 |
| Q8×#41⋊C3 | 3 |
| C32×C4×Q8 | 4 |