Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10590905 | C2 | semidirect |
| 5. #10589367 | C2 | semidirect |
| 6. C3×#4503 | C2 | semidirect |
| 7. #10589117 | C2 | semidirect |
| 33. #4503 | D3 | semidirect |
| 164. C3⋊Dic3 | SD32 | semidirect |
| 272. C32 | #2208 | semidirect |
| 313. C3 | #69234 | semidirect |
| 314. C3 | #71476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#800 | 2 |
| #10590905 | 2 |
| #10590777 | 2 |
| C2×#63547 | 2 |
| #10589367 | 2 |
| C3×#4503 | 2 |
| #10589117 | 2 |
| #71476 | 3 |
| #69234 | 3 |