Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
|---|---|---|
| 71. C32×C8 | Q16 | semidirect |
| 130. C3×C8 | #216 | semidirect |
| 161. C32 | #1707 | semidirect |
| 175. C8 | #3756 | semidirect |
| 187. C3 | #71333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| #10592792 | 2 |
| #10592791 | 2 |
| #10592778 | 2 |
| #10592777 | 2 |
| #10592379 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71333 | 3 |