Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
410 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 88 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. C3×#5075 | C2 | semidirect |
| 3. #10590364 | C2 | semidirect |
| 4. #10590258 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589097 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 28. #5075 | D3 | semidirect |
| 117. C3×C3⋊C8 | SD16 | semidirect |
| 258. C3⋊C8 | #214 | semidirect |
| 321. C32 | #1688 | semidirect |
| 375. C3 | #71025 | semidirect |
| 376. C3 | #71287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5075 | 2 |
| C3×#5073 | 2 |
| #10590364 | 2 |
| #10590258 | 2 |
| #10589410 | 2 |
| #10589097 | 2 |
| #10589090 | 2 |
| #71287 | 3 |
| #71025 | 3 |