Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
167 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 24. C3×C3⋊C16 | C8 | semidirect |
| 66. C3⋊C16 | C3⋊C8 | semidirect |
| 129. C32 | #1371 | semidirect |
| 154. C3 | #67469 | semidirect |
| 155. C3 | #67500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589324 | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×#4458 | 2 |
| #67500 | 3 |
| #67469 | 3 |