Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
456 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 155 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. C27×C4⋊Q8 | C2 | semidirect |
| 2. #11720195 | C2 | semidirect |
| 3. #11720146 | C2 | semidirect |
| 5. C4⋊C4×D27 | C2 | semidirect |
| 6. #11720139 | C2 | semidirect |
| 8. C4×Dic54 | C2 | semidirect |
| 43. D108 | Q8 | semidirect |
| 128. C4⋊Q8 | D27 | semidirect |
| 136. C27 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C4⋊Q8 | 2 |
| #11720195 | 2 |
| #11720146 | 2 |
| #11720142 | 2 |
| C4⋊C4×D27 | 2 |
| #11720139 | 2 |
| C4×D108 | 2 |
| C4×Dic54 | 2 |
| #10589832 | 3 |