Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #10593265 | C2 | semidirect |
| 5. #10593263 | C2 | semidirect |
| 6. C4⋊#3771 | C2 | semidirect |
| 7. C4×#3771 | C2 | semidirect |
| 131. C32 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593738 | 2 |
| C22⋊#3771 | 2 |
| #10593265 | 2 |
| #10593263 | 2 |
| C4⋊#3771 | 2 |
| C4×#3771 | 2 |
| #2164 | 9 |