Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
744 conjugacy classes of subgroups; only the 317 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 317 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 |
|---|---|---|
| 20. C2×C32×Q8 | C8 | semidirect |
| 65. C2×C3×Q8 | C3⋊C8 | semidirect |
| 122. C2×Q8 | C3⋊(C3⋊C8) | semidirect |
| 146. C32 | #1461 | semidirect |
| 179. C3 | #71624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×Q8 | 2 |
| #10592624 | 2 |
| #10589394 | 2 |
| #71624 | 3 |