Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 98 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. C32×#504 | C2 | semidirect |
| 2. C3×#5143 | C2 | semidirect |
| 4. C2×C3×#800 | C2 | semidirect |
| 5. C3×#4517 | C2 | semidirect |
| 6. C3×#4516 | C2 | semidirect |
| 7. C3×#4506 | C2 | semidirect |
| 9. #71455 | C3 | direct (N × H) |
| 27. C3×#504 | D3 | semidirect |
| 28. C3×#504 | C2×C3 | semidirect |
| 31. #5143 | C2×C3 | semidirect |
| 33. C2×#800 | C2×C3 | semidirect |
| 37. #4517 | C2×C3 | semidirect |
| 38. #4516 | C2×C3 | semidirect |
| 39. #4506 | C2×C3 | semidirect |
| 113. #504 | C3×D3 | semidirect |
| 275. C32 | #2223 | semidirect |
| 312. C3 | #71455 | direct (N × H) |
| 313. C3 | C3×#2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#504 | 2 |
| C3×#5143 | 2 |
| C3×#5142 | 2 |
| C2×C3×#800 | 2 |
| C3×#4517 | 2 |
| C3×#4516 | 2 |
| C3×#4506 | 2 |
| C3×#2223 | 3 |
| #71455 | 3 |