Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
221 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 1. C22×#3771 | C2 | semidirect |
| 3. C22⋊#3771 | C2 | semidirect |
| 4. C4⋊#3771 | C2 | semidirect |
| 5. C4×#3771 | C2 | semidirect |
| 24. #3771 | D4 | direct (N × H) |
| 31. C32×D4 | C16 | semidirect |
| 54. C22×C32 | C2×C16 | semidirect |
| 56. C32×C4 | C2×C16 | semidirect |
| 104. C32 | D4×C16 | semidirect |
| 106. D4 | #3771 | direct (N × H) |
| 123. C22 | C2×#3771 | semidirect |
| 129. C4 | C2×#3771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3771 | 2 |
| D4×#622 | 2 |
| C22⋊#3771 | 2 |
| C4⋊#3771 | 2 |
| C4×#3771 | 2 |
| D4×C16 | 9 |