Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 1. C22×#634 | C2 | semidirect |
| 3. C2×#3754 | C2 | semidirect |
| 4. #63657 | C2 | semidirect |
| 5. #63637 | C2 | semidirect |
| 35. #634 | D4 | semidirect |
| 54. C22×C32 | SD16 | semidirect |
| 100. C22×C3 | #214 | semidirect |
| 106. C32 | #448 | semidirect |
| 131. C22 | #3754 | semidirect |
| 137. C3 | #5040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C32×#121 | 2 |
| C2×#3754 | 2 |
| #63657 | 2 |
| #63637 | 2 |
| #5040 | 3 |