Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 7. C2×C3⋊(C3⋊C16) | C4 | semidirect |
| 9. C3×#817 | C4 | semidirect |
| 31. #817 | Dic3 | semidirect |
| 130. C32 | #1384 | semidirect |
| 155. C3 | #67725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63639 | 2 |
| C3×#5106 | 2 |
| #67725 | 3 |