Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
177 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 47. C3×C3⋊C8 | C16 | semidirect |
| 105. C3⋊C8 | C3⋊C16 | semidirect |
| 135. C32 | #1367 | semidirect |
| 161. C3 | #67439 | semidirect |
| 162. C3 | #67554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×C8×C3⋊C8 | 2 |
| #67554 | 3 |
| #67439 | 3 |