Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
138 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 30 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. #5398 | C3 | direct (N × H) |
| 33. C3×A4 | Q16 | semidirect |
| 67. C22×C3 | Dic12 | semidirect |
| 69. A4 | C3×Q16 | semidirect |
| 94. C22 | C3×Dic12 | semidirect |
| 101. C3 | #5398 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4⋊Q8 | 2 |
| C3×C8×A4 | 2 |
| #5398 | 3 |
| C3×#467 | 3 |
| C3×Dic12 | 4 |