Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1137 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1137 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. C3×#5798 | C2 | semidirect |
| 3. C2×C3×#833 | C2 | semidirect |
| 4. #10591096 | C2 | semidirect |
| 5. #10589160 | C2 | semidirect |
| 12. #64149 | C4 | semidirect |
| 24. #5798 | D3 | semidirect |
| 26. C2×#833 | D3 | semidirect |
| 44. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 47. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 50. C3×C4⋊Dic3 | D4 | semidirect |
| 167. C4⋊Dic3 | #67 | semidirect |
| 349. C32 | #1887 | semidirect |
| 408. C3 | #70070 | semidirect |
| 409. C3 | #71650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64149 | 2 |
| C3×#5798 | 2 |
| C2×C3×#833 | 2 |
| #10591096 | 2 |
| #10589160 | 2 |
| #71650 | 3 |
| #70070 | 3 |