Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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×Q16 | C2 | semidirect |
| 3. #64153 | C2 | semidirect |
| 4. C2×#3756 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 22. C2×C3×Q16 | D3 | semidirect |
| 69. C2×Q16 | C3⋊D3 | semidirect |
| 116. C32 | #497 | semidirect |
| 145. C3 | #5190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| #64156 | 2 |
| #64153 | 2 |
| C2×#3756 | 2 |
| C2×#3755 | 2 |
| C2×#3744 | 2 |
| #63642 | 2 |
| #5190 | 3 |