Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
152 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic54 | C2 | semidirect |
| 3. C22⋊C4×C27 | C2 | semidirect |
| 4. #88372 | C2 | semidirect |
| 5. (C2×D27)⋊C4 | C2 | semidirect |
| 6. (C2×D27)⋊C4 | C2 | semidirect |
| 7. C4×Dic27 | C2 | semidirect |
| 72. C27 | #124 | semidirect |
| 92. C22⋊C4 | D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6171 | 2 |
| C2×Dic54 | 2 |
| C22⋊C4×C27 | 2 |
| #88372 | 2 |
| (C2×D27)⋊C4 | 2 |
| C4×Dic27 | 2 |
| #63447 | 3 |