Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×Q8×C27 | C2 | semidirect |
| 4. C4⋊Dic27 | C2 | semidirect |
| 5. Dic27⋊C4 | C2 | semidirect |
| 22. C2×D27 | Q8 | semidirect |
| 53. C27 | C22⋊Q8 | semidirect |
| 65. C2×Q8 | D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C27 | 2 |
| C2×C4×D27 | 2 |
| (C2×D27)⋊C4 | 2 |
| C4⋊Dic27 | 2 |
| Dic27⋊C4 | 2 |
| #63508 | 3 |