Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 73 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×C4×C3⋊D9 | C2 | semidirect |
| 2. C2×C3×D36 | C2 | semidirect |
| 3. C2×#6192 | C2 | semidirect |
| 4. C9×C4⋊Dic3 | C2 | semidirect |
| 5. (C2×D9)⋊Dic3 | C2 | semidirect |
| 22. C2×D36 | D3 | semidirect |
| 30. C2×C3⋊D9 | D4 | semidirect |
| 34. C3×C4×C9 | D4 | semidirect |
| 74. C4⋊Dic3 | D9 | semidirect |
| 98. C4×C9 | #67 | semidirect |
| 102. C3×C9 | #121 | semidirect |
| 162. C3×C4 | D36 | semidirect |
| 170. C9 | #938 | semidirect |
| 202. C4 | #6192 | semidirect |
| 204. C3 | #63457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊D9 | 2 |
| C2×C3×D36 | 2 |
| C2×#6192 | 2 |
| C9×C4⋊Dic3 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| #63916 | 3 |
| #63457 | 3 |