Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 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 |
|---|---|---|
| 3. C3×Q8×Q16 | C3 | semidirect |
| 4. Q16×SL(2,𝔽3) | C3 | direct (N × H) |
| 19. Q8×Q16 | C32 | semidirect |
| 38. C3×SL(2,𝔽3) | Q16 | direct (N × H) |
| 51. C3×Q16 | SL(2,𝔽3) | direct (N × H) |
| 81. C3×Q8 | C3×Q16 | semidirect |
| 90. SL(2,𝔽3) | C3×Q16 | direct (N × H) |
| 100. Q16 | C3×SL(2,𝔽3) | direct (N × H) |
| 125. Q8 | C32×Q16 | semidirect |
| 149. C3 | Q16×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×Q8×SL(2,𝔽3) | 2 |
| C3×C8×SL(2,𝔽3) | 2 |
| C3×Q8×Q16 | 3 |
| Q16×SL(2,𝔽3) | 3 |
| C2×C32×Q16 | 4 |