Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
221 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 221 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 |
|---|---|---|
| 5. #67802 | C3 | direct (N × H) |
| 149. C32 | #1365 | semidirect |
| 176. C3 | #67802 | direct (N × H) |
| 177. C3 | C3×#1365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#500 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#4458 | 2 |
| C3×#1365 | 3 |
| #67802 | 3 |