Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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. C32×#101 | C2 | semidirect |
| 4. #63663 | C2 | semidirect |
| 5. #63651 | C2 | semidirect |
| 20. C3×#101 | D3 | semidirect |
| 61. #101 | C3⋊D3 | direct (N × H) |
| 79. C3⋊D3 | #101 | direct (N × H) |
| 99. C32 | C2×#101 | semidirect |
| 126. C3 | D3×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| M16×C3⋊D3 | 2 |
| C32×#101 | 2 |
| #63663 | 2 |
| #63651 | 2 |
| D3×#101 | 3 |