Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
254 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10590088 | C2 | direct (N × H) |
| 18. C2×#622 | C8 | semidirect |
| 40. #622 | C2×C8 | semidirect |
| 81. C2×C32 | #334 | semidirect |
| 109. C32 | C2×#334 | semidirect |
| 140. C2 | #10590088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63779 | 2 |
| C2×C4×#622 | 2 |
| #10590088 | 2 |
| C2×#334 | 9 |