Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
399 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 114 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×#4699 | C2 | semidirect |
| 4. C3×#4492 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 7. #70892 | C3 | direct (N × H) |
| 24. #4699 | C2×C3 | semidirect |
| 27. #4492 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊C16) | C2×C3 | semidirect |
| 137. C32×C4 | SD32 | semidirect |
| 232. C3×C4 | #827 | semidirect |
| 233. C3×C4 | C3×SD32 | semidirect |
| 239. C32 | #2208 | semidirect |
| 273. C4 | C3×#827 | semidirect |
| 277. C3 | #70892 | direct (N × H) |
| 278. C3 | C3×#2208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C2×C3×#827 | 2 |
| C3×#4699 | 2 |
| C3×#4492 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2208 | 3 |
| #70892 | 3 |