Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
338 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #10590041 | C2 | direct (N × H) |
| 17. C2×#622 | C8 | semidirect |
| 44. #622 | C2×C8 | semidirect |
| 93. C2×C32 | #334 | semidirect |
| 122. C32 | C2×#334 | semidirect |
| 153. C2 | #10590041 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#622 | 2 |
| C2×#63572 | 2 |
| #10590041 | 2 |
| C2×#334 | 9 |