Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
641 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 641 conjugacy classes of subgroups — too many to draw. Only its 260 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 |
|---|---|---|
| 9. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 47. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 75. C32×C4 | #106 | semidirect |
| 133. C3×C4 | #808 | semidirect |
| 137. C32 | #1844 | semidirect |
| 162. C4 | #63574 | semidirect |
| 166. C3 | #69576 | 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×#4935 | 2 |
| C2×#63574 | 2 |
| #69576 | 3 |