Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
362 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 114 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. #10590171 | C2 | direct (N × H) |
| 18. C2×C32×C8 | C8 | semidirect |
| 45. C32×C8 | C2×C8 | semidirect |
| 95. C2×C32 | #335 | semidirect |
| 106. C2×C8 | #622 | semidirect |
| 124. C32 | C2×#335 | semidirect |
| 139. C8 | C2×#622 | semidirect |
| 157. C2 | #10590171 | 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×C8×C3⋊Dic3 | 2 |
| #10590171 | 2 |
| C2×#335 | 9 |