Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
480 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 23. C32×Q16 | C8 | semidirect |
| 62. C3×Q16 | C3⋊C8 | semidirect |
| 105. Q16 | C3⋊(C3⋊C8) | semidirect |
| 122. C32 | #1579 | semidirect |
| 145. C3 | #70902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| Q8×C3⋊(C3⋊C8) | 2 |
| #10589401 | 2 |
| #10589323 | 2 |
| #10589321 | 2 |
| #70902 | 3 |