Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C4×D27 | C2 | semidirect |
| 3. C42×C27 | C2 | semidirect |
| 4. (C2×D27)⋊C4 | C2 | semidirect |
| 5. C4⋊Dic27 | C2 | semidirect |
| 12. D108 | C4 | direct (N × H) |
| 22. C2×D27 | C2×C4 | semidirect |
| 24. C4×C27 | C2×C4 | semidirect |
| 25. C4×C27 | D4 | semidirect |
| 53. C27 | C4×D4 | semidirect |
| 69. C42 | D27 | semidirect |
| 96. C4 | C4×D27 | semidirect |
| 97. C4 | D108 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D108 | 2 |
| C2×C4×D27 | 2 |
| C42×C27 | 2 |
| (C2×D27)⋊C4 | 2 |
| C4⋊Dic27 | 2 |
| C4×D36 | 3 |