Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
347 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 347 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #11720775 | C2 | direct (N × H) |
| 8. C2×C8×H(3,𝔽3) | C4 | semidirect |
| 9. C2×#6180 | C4 | semidirect |
| 10. C8×#272 | C4 | semidirect |
| 22. C8×H(3,𝔽3) | C2×C4 | semidirect |
| 23. #6180 | C2×C4 | semidirect |
| 54. C2×H(3,𝔽3) | #107 | semidirect |
| 56. #272 | #107 | semidirect |
| 84. H(3,𝔽3) | C2×#107 | semidirect |
| 115. C2×C8 | #1088 | semidirect |
| 148. C8 | C2×#1088 | semidirect |
| 174. C2 | #11720775 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#1088 | 2 |
| C2×C8×#272 | 2 |
| #11720775 | 2 |
| C2×C3×#107 | 9 |