Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
268 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 26. C4×H(3,𝔽3) | Q8 | semidirect |
| 28. #1084 | Q8 | semidirect |
| 72. C32×C4 | Dic6 | semidirect |
| 73. C32×C4 | Dic6 | semidirect |
| 85. H(3,𝔽3) | C4⋊Q8 | semidirect |
| 144. C32 | #888 | semidirect |
| 145. C32 | #888 | semidirect |
| 169. C4 | #6196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6196 | 2 |
| C4×#1084 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| #88449 | 2 |
| #63918 | 3 |