Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 147 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×D27 | C2 | semidirect |
| 3. C27×#124 | C2 | semidirect |
| 4. #11720193 | C2 | semidirect |
| 5. #11720185 | C2 | semidirect |
| 6. #11720132 | C2 | semidirect |
| 7. #11720127 | C2 | semidirect |
| 8. #11720121 | C2 | semidirect |
| 9. #11720118 | C2 | semidirect |
| 157. #124 | D27 | semidirect |
| 161. C27 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D27 | 2 |
| C2×#88401 | 2 |
| C27×#124 | 2 |
| #11720193 | 2 |
| #11720185 | 2 |
| #11720132 | 2 |
| #11720127 | 2 |
| #11720121 | 2 |
| #11720118 | 2 |
| #10589777 | 3 |