Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
313 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 313 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 |
|---|---|---|
| 3. #10590812 | C2 | semidirect |
| 5. #10589137 | C2 | semidirect |
| 6. #10589129 | C2 | semidirect |
| 7. #10589105 | C2 | semidirect |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#827 | C4 | semidirect |
| 74. #829 | Dic3 | semidirect |
| 75. #827 | Dic3 | semidirect |
| 250. C32 | #2180 | semidirect |
| 283. C3 | #70928 | semidirect |
| 284. C3 | #71521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5197 | 2 |
| C3×#5195 | 2 |
| #10590812 | 2 |
| #10589432 | 2 |
| #10589137 | 2 |
| #10589129 | 2 |
| #10589105 | 2 |
| #71521 | 3 |
| #70928 | 3 |