Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
175 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 175 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C3×Dic6 | C2 | semidirect |
| 4. C3×C4⋊Dic3 | C2 | semidirect |
| 5. C3×Dic3⋊C4 | C2 | semidirect |
| 7. #924 | C3 | direct (N × H) |
| 19. C2×Dic6 | C2×C3 | semidirect |
| 24. C4⋊Dic3 | C2×C3 | semidirect |
| 25. Dic3⋊C4 | C2×C3 | semidirect |
| 28. C22×C32 | Q8 | semidirect |
| 70. C22×C3 | Dic6 | semidirect |
| 71. C22×C3 | C3×Q8 | semidirect |
| 84. C32 | C22⋊Q8 | semidirect |
| 106. C22 | C3×Dic6 | semidirect |
| 113. C3 | #924 | direct (N × H) |
| 114. C3 | C3×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4 | 2 |
| C2×C3×Dic6 | 2 |
| C3×#217 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C22⋊Q8 | 3 |
| #924 | 3 |