Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
349 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C3×Dic24 | C2 | semidirect |
| 4. C3×#4873 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4492 | C2 | semidirect |
| 9. #69205 | C3 | direct (N × H) |
| 29. C2×Dic24 | C2×C3 | semidirect |
| 30. #4873 | C2×C3 | semidirect |
| 36. Dic3⋊C16 | C2×C3 | semidirect |
| 37. #4492 | C2×C3 | semidirect |
| 273. C32 | #2211 | semidirect |
| 314. C3 | #69205 | direct (N × H) |
| 315. C3 | C3×#2211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5155 | 2 |
| C2×C3×#827 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4873 | 2 |
| C32×#357 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4492 | 2 |
| C3×#2211 | 3 |
| #69205 | 3 |