Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
424 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 424 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. C27×C4⋊Q8 | C2 | semidirect |
| 3. Q8×Dic27 | C2 | semidirect |
| 4. #11720147 | C2 | semidirect |
| 5. #11720146 | C2 | semidirect |
| 6. #11720141 | C2 | semidirect |
| 8. C4×Dic54 | C2 | semidirect |
| 126. C4⋊Q8 | D27 | semidirect |
| 134. C27 | #556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C27×C4⋊Q8 | 2 |
| #11720196 | 2 |
| Q8×Dic27 | 2 |
| #11720147 | 2 |
| #11720146 | 2 |
| #11720141 | 2 |
| C4×D108 | 2 |
| C4×Dic54 | 2 |
| #10589834 | 3 |