Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
331 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 132 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×#634 | C2 | semidirect |
| 3. C2×C3×Dic6 | C2 | semidirect |
| 4. C2×#627 | C2 | semidirect |
| 6. D3×Dic6 | C2 | direct (N × H) |
| 12. #634 | C22 | semidirect |
| 16. C3×Dic6 | C22 | semidirect |
| 17. #627 | C22 | semidirect |
| 31. C2×Dic6 | D3 | direct (N × H) |
| 33. C2×C3×D3 | Q8 | semidirect |
| 62. Dic6 | C2×D3 | direct (N × H) |
| 63. C2×C32 | C2×Q8 | semidirect |
| 65. C3×D3 | C2×Q8 | semidirect |
| 77. C2×D3 | Dic6 | direct (N × H) |
| 89. C32 | C22×Q8 | semidirect |
| 103. C2×C3 | C2×Dic6 | semidirect |
| 104. C2×C3 | D3×Q8 | semidirect |
| 107. D3 | C2×Dic6 | direct (N × H) |
| 116. C3 | C22×Dic6 | semidirect |
| 117. C3 | C2×D3×Q8 | semidirect |
| 119. C2 | D3×Dic6 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#634 | 2 |
| C2×C3×C4×D3 | 2 |
| C2×C3×Dic6 | 2 |
| C2×#627 | 2 |
| C2×D3×Dic3 | 2 |
| D3×Dic6 | 2 |
| C2×D3×Q8 | 3 |
| C22×Dic6 | 3 |