Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
444 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 115 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. C32×#472 | C2 | semidirect |
| 2. C2×#63653 | C2 | semidirect |
| 3. #10592841 | C2 | semidirect |
| 4. #10592839 | C2 | semidirect |
| 5. #10589429 | C2 | semidirect |
| 6. #10589361 | C2 | semidirect |
| 7. #10589359 | C2 | semidirect |
| 24. C3×#472 | D3 | semidirect |
| 86. #472 | C3⋊D3 | semidirect |
| 184. C32 | #2221 | semidirect |
| 215. C3 | #71092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#472 | 2 |
| C2×#63653 | 2 |
| #10592841 | 2 |
| #10592839 | 2 |
| #10589429 | 2 |
| #10589361 | 2 |
| #10589359 | 2 |
| #71092 | 3 |