Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
319 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 37. C3×C3⋊C16 | Q8 | semidirect |
| 65. #634 | C16 | semidirect |
| 104. C3⋊C16 | Dic6 | semidirect |
| 185. C32 | Q8×C16 | semidirect |
| 213. C3 | C16×Dic6 | semidirect |
| 214. C3 | #69280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#634 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589133 | 2 |
| #10589102 | 2 |
| #69280 | 3 |
| C16×Dic6 | 3 |