Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
330 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 88 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. #88550 | C2 | direct (N × H) |
| 33. C2×H(3,𝔽3) | Q16 | semidirect |
| 49. H(3,𝔽3) | C2×Q16 | semidirect |
| 66. C2×C32 | #216 | semidirect |
| 82. C32 | C2×#216 | semidirect |
| 102. C2 | #88550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×H(3,𝔽3) | 2 |
| C2×#6229 | 2 |
| #88550 | 2 |
| C2×#6180 | 2 |
| C2×C3×#216 | 3 |