Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 181. C32 | #2241 | semidirect |
| 209. C3 | #69065 | semidirect |
| 210. C3 | #71382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592398 | 2 |
| C3×#4682 | 2 |
| C3×C4×C3⋊C16 | 2 |
| #10589119 | 2 |
| #71382 | 3 |
| #69065 | 3 |