Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. C22×#3771 | C2 | semidirect |
| 3. C22⋊#3771 | C2 | direct (N × H) |
| 11. C2×#3771 | C22 | semidirect |
| 31. C23×C32 | C16 | semidirect |
| 61. C22×C32 | C2×C16 | semidirect |
| 91. C2×C32 | C22⋊C16 | semidirect |
| 122. C32 | C2×C22⋊C16 | semidirect |
| 125. C23 | #3771 | semidirect |
| 149. C22 | C2×#3771 | semidirect |
| 159. C2 | C22⋊#3771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#622 | 2 |
| C22×#3771 | 2 |
| C22⋊#3771 | 2 |
| C2×C22⋊C16 | 9 |