Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
396 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 86 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×D4×SL(2,𝔽3) | C2 | semidirect |
| 2. C3×C8×SL(2,𝔽3) | C2 | semidirect |
| 3. C3×Q8×D8 | C3 | semidirect |
| 4. D8×SL(2,𝔽3) | C3 | direct (N × H) |
| 8. C3×D4×Q8 | C2×C3 | semidirect |
| 9. D4×SL(2,𝔽3) | C2×C3 | semidirect |
| 12. C3×C8×Q8 | C2×C3 | semidirect |
| 14. C8×SL(2,𝔽3) | C2×C3 | semidirect |
| 20. Q8×D8 | C32 | semidirect |
| 39. C3×SL(2,𝔽3) | D8 | direct (N × H) |
| 41. D4×Q8 | C2×C32 | semidirect |
| 44. C8×Q8 | C2×C32 | semidirect |
| 56. C3×D8 | SL(2,𝔽3) | direct (N × H) |
| 87. C3×Q8 | C3×D8 | semidirect |
| 91. C3×D4 | C2×SL(2,𝔽3) | semidirect |
| 99. SL(2,𝔽3) | C3×D8 | direct (N × H) |
| 102. C3×C8 | C2×SL(2,𝔽3) | semidirect |
| 113. D8 | C3×SL(2,𝔽3) | direct (N × H) |
| 142. Q8 | C32×D8 | semidirect |
| 144. D4 | C2×C3×SL(2,𝔽3) | semidirect |
| 152. C8 | C2×C3×SL(2,𝔽3) | semidirect |
| 172. C3 | D8×SL(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×SL(2,𝔽3) | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| C3×Q8×D8 | 3 |
| D8×SL(2,𝔽3) | 3 |
| C2×C32×D8 | 4 |