Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
900 conjugacy classes of subgroups; only the 569 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 569 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 |
|---|---|---|
| 15. C32×C42 | C8 | semidirect |
| 40. C3×C42 | C3⋊C8 | semidirect |
| 48. C32×C4 | C4⋊C8 | semidirect |
| 73. C42 | C3⋊(C3⋊C8) | semidirect |
| 80. C3×C4 | C4⋊(C3⋊C8) | semidirect |
| 83. C32 | #1842 | semidirect |
| 100. C4 | C4⋊(C3⋊(C3⋊C8)) | semidirect |
| 103. C3 | #69394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C43 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #69394 | 3 |