Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
351 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 351 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 |
|---|---|---|
| 2. C3×#4682 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 7. #70886 | C3 | direct (N × H) |
| 21. #4682 | C2×C3 | semidirect |
| 26. #4489 | C2×C3 | semidirect |
| 27. C4⋊(C3⋊C16) | C2×C3 | semidirect |
| 32. C32×D8 | Q8 | semidirect |
| 95. C3×D8 | Dic6 | semidirect |
| 96. C3×D8 | C3×Q8 | semidirect |
| 182. D8 | C3×Dic6 | semidirect |
| 220. C32 | #2224 | semidirect |
| 257. C3 | #70886 | direct (N × H) |
| 258. C3 | C3×#2224 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| C3×#4682 | 2 |
| C3×#4562 | 2 |
| C3×#4489 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#2224 | 3 |
| #70886 | 3 |