Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
418 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. C4⋊#1084 | C2 | semidirect |
| 4. C4×#1084 | C2 | semidirect |
| 7. C2×C4×H(3,𝔽3) | C4 | semidirect |
| 24. C2×C32×C4 | Dic3 | semidirect |
| 46. H(3,𝔽3) | #117 | semidirect |
| 76. C32 | #926 | semidirect |
| 79. C2×C4 | #1084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×H(3,𝔽3) | 2 |
| #88552 | 2 |
| C4⋊#1084 | 2 |
| C4×#1084 | 2 |
| C3×#926 | 3 |