Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
840 conjugacy classes of subgroups; only the 497 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 497 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. C32×C4×C8 | C4 | semidirect |
| 29. C3×C4×C8 | Dic3 | semidirect |
| 40. C32×C8 | C4⋊C4 | semidirect |
| 58. C32×C4 | #106 | semidirect |
| 67. C4×C8 | C3⋊Dic3 | semidirect |
| 77. C3×C8 | C4⋊Dic3 | semidirect |
| 96. C3×C4 | #817 | semidirect |
| 100. C32 | #1844 | semidirect |
| 110. C8 | C4⋊(C3⋊Dic3) | semidirect |
| 120. C4 | #63644 | semidirect |
| 123. C3 | #69764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×C8 | 2 |
| C2×#63644 | 2 |
| #10592634 | 2 |
| #69764 | 3 |