Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 25. C3⋊Dic9 | Q8 | semidirect |
| 61. C3×C9 | C4⋊Q8 | semidirect |
| 93. C9 | #944 | semidirect |
| 109. C3 | #63506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C2×#6226 | 2 |
| #88534 | 2 |
| C4×C3⋊Dic9 | 2 |
| #64153 | 3 |
| #63506 | 3 |