Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 110 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×#494 | C2 | semidirect |
| 4. C3×#4564 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 7. #71315 | C3 | direct (N × H) |
| 20. C3×#494 | D3 | semidirect |
| 21. C3×#494 | C2×C3 | semidirect |
| 27. #4564 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊C16) | C2×C3 | semidirect |
| 85. #494 | C3×D3 | semidirect |
| 136. C32×C4 | SD32 | semidirect |
| 226. C3×C4 | #828 | semidirect |
| 227. C3×C4 | C3×SD32 | semidirect |
| 233. C32 | #2208 | semidirect |
| 266. C4 | C3×#828 | semidirect |
| 270. C3 | #71315 | direct (N × H) |
| 271. C3 | C3×#2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#494 | 2 |
| C2×C3×#828 | 2 |
| C3×C4×D24 | 2 |
| C3×#4564 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2208 | 3 |
| #71315 | 3 |