Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1085 conjugacy classes of subgroups; only the 404 normal subgroups are shown.
This group has 1085 conjugacy classes of subgroups — too many to draw. Only its 404 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. #10591139 | C2 | semidirect |
| 4. #10591138 | C2 | semidirect |
| 5. C2×#63576 | C2 | semidirect |
| 8. #64157 | C4 | semidirect |
| 33. #3748 | C2×C4 | semidirect |
| 34. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 193. C32 | #2913 | semidirect |
| 224. C3 | #82562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64157 | 2 |
| C3×#5827 | 2 |
| #10591139 | 2 |
| #10591138 | 2 |
| C2×#63576 | 2 |
| #82562 | 3 |