Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
442 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
| 10. C8×C3⋊Dic3 | C4 | semidirect |
| 11. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 42. C32×C8 | C4⋊C4 | semidirect |
| 43. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 62. C32×C4 | #107 | semidirect |
| 64. C3⋊Dic3 | #107 | semidirect |
| 73. C4×C8 | #157 | semidirect |
| 111. C32 | #1845 | semidirect |
| 124. C8 | C4⋊#157 | semidirect |
| 138. C4 | #63769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63769 | 2 |
| #10593735 | 2 |
| C4×C8×C3⋊D3 | 2 |
| #1845 | 9 |