Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 65 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. #10590042 | C2 | semidirect |
| 4. #10590041 | C2 | semidirect |
| 128. C32 | #1568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#622 | 2 |
| #10591066 | 2 |
| #10590042 | 2 |
| #10590041 | 2 |
| #1568 | 9 |