Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
566 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#64243 | C2 | semidirect |
| 5. #10593557 | C2 | direct (N × H) |
| 6. C2×#63746 | C2 | semidirect |
| 7. C2×#63745 | C2 | semidirect |
| 8. C2×#63744 | C2 | semidirect |
| 23. #64243 | C22 | semidirect |
| 26. #63746 | C22 | semidirect |
| 27. #63745 | C22 | semidirect |
| 28. #63744 | C22 | semidirect |
| 174. C2×C32 | #478 | semidirect |
| 177. C3⋊D3 | #478 | semidirect |
| 229. C32 | C2×#478 | semidirect |
| 296. C2 | #10593557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×#64243 | 2 |
| C2×#63782 | 2 |
| #10593557 | 2 |
| C2×#63746 | 2 |
| C2×#63745 | 2 |
| C2×#63744 | 2 |
| C2×#478 | 9 |