Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
139 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 139 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×C32×Q8 | C2 | semidirect |
| 3. C3×#216 | C2 | semidirect |
| 4. C3×#215 | C2 | semidirect |
| 5. C3×#208 | C2 | semidirect |
| 7. #942 | C3 | direct (N × H) |
| 19. C2×C3×Q8 | D3 | semidirect |
| 20. C2×C3×Q8 | C2×C3 | semidirect |
| 25. #216 | C2×C3 | semidirect |
| 26. #215 | C2×C3 | semidirect |
| 27. #208 | C2×C3 | semidirect |
| 61. C2×Q8 | C3×D3 | semidirect |
| 81. C32 | #137 | semidirect |
| 106. C3 | #942 | direct (N × H) |
| 107. C3 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q8 | 2 |
| C3×#235 | 2 |
| C3×#216 | 2 |
| C3×#215 | 2 |
| C3×#208 | 2 |
| C3×#137 | 3 |
| #942 | 3 |