Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 131 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×C32×Q8 | C2 | semidirect |
| 2. C2×#3755 | C2 | semidirect |
| 4. #63662 | C2 | semidirect |
| 5. #63657 | C2 | semidirect |
| 18. C22×C3×Q8 | D3 | semidirect |
| 27. C32×Q8 | D4 | semidirect |
| 51. C22×C32 | SD16 | semidirect |
| 60. C22×Q8 | C3⋊D3 | semidirect |
| 69. C3×Q8 | #67 | semidirect |
| 97. C22×C3 | #215 | semidirect |
| 106. C32 | #448 | semidirect |
| 111. Q8 | #638 | semidirect |
| 131. C22 | #3755 | semidirect |
| 137. C3 | #5227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C2×#3755 | 2 |
| #64139 | 2 |
| #63662 | 2 |
| #63657 | 2 |
| #5227 | 3 |