Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 76 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×#5125 | C2 | semidirect |
| 3. #10589419 | C2 | semidirect |
| 4. #10589138 | C2 | semidirect |
| 5. #10589126 | C2 | semidirect |
| 20. #5125 | D3 | semidirect |
| 206. C32 | #2238 | semidirect |
| 242. C3 | #70723 | semidirect |
| 243. C3 | #71088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5135 | 2 |
| C3×#5125 | 2 |
| #10589419 | 2 |
| #10589138 | 2 |
| #10589126 | 2 |
| #71088 | 3 |
| #70723 | 3 |