Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #64078 | C2 | semidirect |
| 4. #63637 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 51. C32×C4 | SD16 | semidirect |
| 92. C3×C4 | #214 | semidirect |
| 96. C32 | #461 | semidirect |
| 120. C4 | #3754 | semidirect |
| 123. C3 | #5019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×D4 | 2 |
| C2×#3754 | 2 |
| #64078 | 2 |
| #63637 | 2 |
| C4⋊(C3⋊(C3⋊C8)) | 2 |
| #5019 | 3 |