Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1944 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 1944 conjugacy classes of subgroups — too many to draw. Only its 537 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. #10592919 | C2 | semidirect |
| 3. #10592636 | C2 | semidirect |
| 7. C32×#127 | C4 | semidirect |
| 17. C2×C32×D4 | C2×C4 | semidirect |
| 21. C32×C42 | C2×C4 | semidirect |
| 26. C3×#127 | Dic3 | semidirect |
| 45. C2×C3×D4 | C2×Dic3 | semidirect |
| 49. C3×C42 | C2×Dic3 | semidirect |
| 60. #127 | C3⋊Dic3 | semidirect |
| 79. C2×D4 | C2×C3⋊Dic3 | semidirect |
| 84. C42 | C2×C3⋊Dic3 | semidirect |
| 92. C32 | #2380 | semidirect |
| 112. C3 | #83174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| #10592919 | 2 |
| #10592636 | 2 |
| #83174 | 3 |