Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
840 conjugacy classes of subgroups; only the 377 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 377 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 |
|---|---|---|
| 13. C4×C3⋊(C3⋊C8) | C4 | semidirect |
| 52. C3⋊(C3⋊C8) | C4⋊C4 | semidirect |
| 76. C32×C4 | #107 | semidirect |
| 125. C3×C4 | #807 | semidirect |
| 129. C32 | #1845 | semidirect |
| 155. C4 | #63634 | semidirect |
| 158. C3 | #69577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#384 | 2 |
| C2×#63634 | 2 |
| #10592634 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #69577 | 3 |