Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
600 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 149 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. #10592777 | C2 | semidirect |
| 3. #10592719 | C2 | semidirect |
| 5. #10589413 | C2 | semidirect |
| 6. #10589401 | C2 | semidirect |
| 220. C32 | #1650 | semidirect |
| 261. C3 | #71933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#556 | 2 |
| #10592777 | 2 |
| #10592719 | 2 |
| #10592718 | 2 |
| #10589413 | 2 |
| #10589401 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #71933 | 3 |