Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 222. C32 | #2229 | semidirect |
| 254. C3 | #70912 | semidirect |
| 255. C3 | #71357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| C3×#4683 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #10589142 | 2 |
| #10589140 | 2 |
| #10589117 | 2 |
| #71357 | 3 |
| #70912 | 3 |