Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1422 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 303 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. C42×D32 | C2 | semidirect |
| 3. C42×#157 | C2 | semidirect |
| 4. C4×#3773 | C2 | semidirect |
| 5. C4×D32⋊C4 | C2 | semidirect |
| 12. C4×GO+(4,𝔽2) | C4 | direct (N × H) |
| 28. C4×D32 | C2×C4 | semidirect |
| 30. C4×#157 | C2×C4 | semidirect |
| 31. #3773 | C2×C4 | semidirect |
| 32. D32⋊C4 | C2×C4 | semidirect |
| 33. C32×C42 | D4 | semidirect |
| 34. C4×C3⋊Dic3 | D4 | semidirect |
| 52. GO+(4,𝔽2) | C42 | direct (N × H) |
| 86. D32 | C2×C42 | semidirect |
| 88. #157 | C2×C42 | semidirect |
| 89. C32×C4 | C4×D4 | semidirect |
| 90. C3⋊Dic3 | C4×D4 | semidirect |
| 142. C42 | GO+(4,𝔽2) | direct (N × H) |
| 154. C32 | C42×D4 | semidirect |
| 187. C4 | C4×GO+(4,𝔽2) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×GO+(4,𝔽2) | 2 |
| C42×D32 | 2 |
| C42×#157 | 2 |
| C4×#3773 | 2 |
| C4×D32⋊C4 | 2 |
| C42×D4 | 9 |