Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 8. #6180 | C4 | semidirect |
| 9. (C3⋊(C3⋊C8))⋊C3 | C4 | semidirect |
| 20. (C3⋊Dic3)⋊C3 | C8 | semidirect |
| 29. C3⋊(C3⋊C8) | Dic3 | semidirect |
| 55. C3⋊Dic3 | C3⋊C8 | semidirect |
| 58. H(3,𝔽3) | C4×C8 | semidirect |
| 98. C32 | C4×C3⋊C8 | semidirect |
| 99. C32 | C8×Dic3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6180 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #63553 | 3 |
| Dic3×C3⋊C8 | 3 |