Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
360 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. Q8×C3⋊Dic3 | C2 | semidirect |
| 4. #63662 | C2 | semidirect |
| 6. #63645 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 12. C32×SD16 | C4 | semidirect |
| 30. C32×Q8 | C2×C4 | semidirect |
| 40. C32×C8 | C2×C4 | semidirect |
| 46. C3×SD16 | Dic3 | semidirect |
| 75. C3×Q8 | C2×Dic3 | semidirect |
| 85. C3×C8 | C2×Dic3 | semidirect |
| 94. SD16 | C3⋊Dic3 | semidirect |
| 114. C32 | #440 | semidirect |
| 117. Q8 | C2×C3⋊Dic3 | semidirect |
| 128. C8 | C2×C3⋊Dic3 | semidirect |
| 144. C3 | #5164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×SD16 | 2 |
| Q8×C3⋊Dic3 | 2 |
| D4×C3⋊Dic3 | 2 |
| #63662 | 2 |
| #63659 | 2 |
| #63645 | 2 |
| #63642 | 2 |
| #5164 | 3 |