Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #88993 | C2 | direct (N × H) |
| 3. C2×C3⋊#622 | C2 | semidirect |
| 10. C3⋊#622 | C22 | semidirect |
| 35. C2×C33 | M16 | semidirect |
| 57. C33 | C2×M16 | semidirect |
| 77. C2×C32 | #208 | semidirect |
| 99. C32 | C2×#208 | semidirect |
| 113. C2×C3 | #3792 | semidirect |
| 123. C3 | C2×#3792 | semidirect |
| 125. C2 | #88993 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊Dic3 | 2 |
| #88993 | 2 |
| C2×C3⋊#622 | 2 |
| C2×#3792 | 3 |
| C2×#208 | 9 |