Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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. Q8×C3⋊Dic3 | C2 | semidirect |
| 4. C32×#103 | C2 | semidirect |
| 6. #63642 | C2 | semidirect |
| 7. #63634 | C2 | semidirect |
| 14. #3755 | C4 | semidirect |
| 24. C3×#103 | D3 | semidirect |
| 30. C32×Q8 | C2×C4 | semidirect |
| 41. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 70. #103 | C3⋊D3 | semidirect |
| 75. C3×Q8 | C4×D3 | semidirect |
| 114. C32 | #440 | semidirect |
| 117. Q8 | C4×C3⋊D3 | semidirect |
| 144. C3 | #4817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic3 | 2 |
| C2×#3755 | 2 |
| #64102 | 2 |
| C32×#103 | 2 |
| #63648 | 2 |
| #63642 | 2 |
| #63634 | 2 |
| #4817 | 3 |