Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
445 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 445 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 57. C3×C3⋊C8 | Q16 | semidirect |
| 117. C3⋊C8 | Dic12 | semidirect |
| 143. C32 | #1713 | semidirect |
| 164. C3 | #68065 | semidirect |
| 165. C3 | #71298 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592398 | 2 |
| C3×#4699 | 2 |
| #10590311 | 2 |
| C3×C8×C3⋊C8 | 2 |
| #71298 | 3 |
| #68065 | 3 |