Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
408 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 137 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. #10592382 | C2 | semidirect |
| 5. #10589356 | C2 | semidirect |
| 6. #10589355 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 154. C32 | #2228 | semidirect |
| 183. C3 | #70888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D8 | 2 |
| #10592382 | 2 |
| #10589428 | 2 |
| #10589356 | 2 |
| #10589355 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #70888 | 3 |