Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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. #11720158 | C2 | semidirect |
| 3. C2×#88360 | C2 | semidirect |
| 4. #11720151 | C2 | semidirect |
| 5. C27×#108 | C2 | semidirect |
| 6. #11720064 | C2 | semidirect |
| 7. #11720063 | C2 | semidirect |
| 126. #108 | D27 | semidirect |
| 129. C27 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720158 | 2 |
| #11720157 | 2 |
| C2×#88360 | 2 |
| #11720151 | 2 |
| C27×#108 | 2 |
| #11720064 | 2 |
| #11720063 | 2 |
| #10588578 | 3 |