Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
223 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 223 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 |
|---|---|---|
| 5. #67474 | C3 | direct (N × H) |
| 158. C32 | #1362 | semidirect |
| 186. C3 | #67474 | direct (N × H) |
| 187. C3 | C3×#1362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4699 | 2 |
| C32×#335 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×#1362 | 3 |
| #67474 | 3 |