Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11720198 | C2 | semidirect |
| 3. #11720158 | C2 | semidirect |
| 4. #11720118 | C2 | semidirect |
| 5. C27×#104 | C2 | semidirect |
| 6. #11720063 | C2 | semidirect |
| 7. #11720045 | C2 | semidirect |
| 149. #104 | D27 | semidirect |
| 151. C27 | #456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720676 | 2 |
| #11720198 | 2 |
| #11720158 | 2 |
| #11720118 | 2 |
| C27×#104 | 2 |
| #11720063 | 2 |
| #11720045 | 2 |
| #10588506 | 3 |