Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
373 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 373 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 161. C32 | #1292 | semidirect |
| 197. C3 | #67711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| C3×#4924 | 2 |
| #67711 | 3 |