Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
300 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 109 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. C32×#346 | C2 | semidirect |
| 3. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 13. C3×#346 | D3 | semidirect |
| 49. #346 | C3⋊D3 | semidirect |
| 115. C32 | #1330 | semidirect |
| 141. C3 | #67515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592387 | 2 |
| C32×#346 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #67515 | 3 |