Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
420 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 8. C32×#107 | C4 | semidirect |
| 11. #63644 | C4 | semidirect |
| 13. #63639 | C4 | semidirect |
| 36. C3×#107 | Dic3 | semidirect |
| 90. #107 | C3⋊Dic3 | semidirect |
| 136. C32 | #1386 | semidirect |
| 165. C3 | #67726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#427 | 2 |
| C2×#63644 | 2 |
| C2×#63639 | 2 |
| #67726 | 3 |