Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
315 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 315 conjugacy classes of subgroups — too many to draw. Only its 72 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. #10590932 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 4. #10590621 | C2 | semidirect |
| 5. #10589362 | C2 | semidirect |
| 6. C3×#4493 | C2 | semidirect |
| 7. #10589126 | C2 | semidirect |
| 39. #4493 | D3 | semidirect |
| 269. C32 | #2223 | semidirect |
| 305. C3 | #69363 | semidirect |
| 306. C3 | #71093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4897 | 2 |
| #10590932 | 2 |
| C2×#63548 | 2 |
| #10590621 | 2 |
| #10589362 | 2 |
| C3×#4493 | 2 |
| #10589126 | 2 |
| #71093 | 3 |
| #69363 | 3 |