Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
238 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 89 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. #10593265 | C2 | semidirect |
| 4. C4⋊#3771 | C2 | semidirect |
| 39. C4×C3⋊D3 | C16 | semidirect |
| 64. C32×C4 | C2×C16 | semidirect |
| 66. C3⋊Dic3 | C2×C16 | semidirect |
| 92. C3⋊D3 | C4⋊C16 | semidirect |
| 119. C32 | C2×C4⋊C16 | semidirect |
| 149. C4 | #64213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64213 | 2 |
| C4×#3787 | 2 |
| #10593265 | 2 |
| C4⋊#3771 | 2 |
| C2×C4⋊C16 | 9 |