Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
840 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 1. C32×#493 | C2 | semidirect |
| 2. #10592772 | C2 | semidirect |
| 3. #10592394 | C2 | semidirect |
| 4. C8×C3⋊(C3⋊C8) | C2 | semidirect |
| 13. C3×#493 | D3 | semidirect |
| 43. C32×C8 | D8 | semidirect |
| 44. C3⋊(C3⋊C8) | D8 | semidirect |
| 47. #493 | C3⋊D3 | semidirect |
| 81. C3×C8 | #213 | semidirect |
| 104. C32 | #1712 | semidirect |
| 114. C8 | #3753 | semidirect |
| 126. C3 | #71276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#493 | 2 |
| #10592772 | 2 |
| #10592394 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #71276 | 3 |