Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
558 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C32×C4⋊C4 | C2 | semidirect |
| 4. C2×#3750 | C2 | semidirect |
| 5. #63658 | C2 | semidirect |
| 16. C2×C3×C4⋊C4 | D3 | semidirect |
| 62. C2×C4⋊C4 | C3⋊D3 | semidirect |
| 111. C32 | #399 | semidirect |
| 148. C3 | #4993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊C4 | 2 |
| C2×#3752 | 2 |
| C2×#3750 | 2 |
| #63658 | 2 |
| #4993 | 3 |