Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
748 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 145 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. #10593657 | C2 | direct (N × H) |
| 3. C2×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 6. C2×C3×#41⋊C3 | C4 | semidirect |
| 7. C2×C3×#41⋊C3 | C4 | semidirect |
| 10. C22×C3×SL(2,𝔽3) | C4 | semidirect |
| 12. C3⋊GU(2,𝔽3) | C22 | semidirect |
| 25. C3×#41⋊C3 | C2×C4 | semidirect |
| 28. C2×C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 43. C2×#41⋊C3 | Dic3 | semidirect |
| 44. C2×#41⋊C3 | Dic3 | semidirect |
| 47. C22×SL(2,𝔽3) | Dic3 | semidirect |
| 114. #41⋊C3 | C2×Dic3 | semidirect |
| 117. C2×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 320. C2×C3 | #5423 | semidirect |
| 340. C3 | C2×#5423 | semidirect |
| 345. C2 | #10593657 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#41⋊C3 | 2 |
| #10593657 | 2 |
| C2×C3⋊GU(2,𝔽3) | 2 |
| C2×#5423 | 3 |
| C2×#5236 | 3 |
| C2×#3748 | 4 |