Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
580 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 183 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. C27×C4⋊Q8 | C2 | semidirect |
| 3. #11720193 | C2 | semidirect |
| 5. #11720137 | C2 | semidirect |
| 7. #11720118 | C2 | semidirect |
| 39. C4×D27 | Q8 | semidirect |
| 61. C4×C27 | C2×Q8 | semidirect |
| 64. Dic27 | C2×Q8 | semidirect |
| 88. D27 | C4⋊Q8 | direct (N × H) |
| 115. C4⋊Q8 | D27 | direct (N × H) |
| 118. C27 | C2×C4⋊Q8 | semidirect |
| 182. C4 | Q8×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D27 | 2 |
| C27×C4⋊Q8 | 2 |
| #11720193 | 2 |
| C4⋊C4×D27 | 2 |
| #11720137 | 2 |
| C42×D27 | 2 |
| #11720118 | 2 |
| D9×C4⋊Q8 | 3 |