Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1123 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1123 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 5. #11721117 | C2 | direct (N × H) |
| 24. C2×C4×H(3,𝔽3) | Q8 | semidirect |
| 27. C2×#1084 | Q8 | semidirect |
| 54. C4×H(3,𝔽3) | C2×Q8 | semidirect |
| 56. #1084 | C2×Q8 | semidirect |
| 74. C2×C32×C4 | Dic6 | semidirect |
| 90. C2×H(3,𝔽3) | C4⋊Q8 | semidirect |
| 127. C32×C4 | C2×Dic6 | semidirect |
| 139. H(3,𝔽3) | C2×C4⋊Q8 | semidirect |
| 173. C2×C32 | #888 | semidirect |
| 211. C32 | C2×#888 | semidirect |
| 220. C2×C4 | #6196 | semidirect |
| 241. C4 | C2×#6196 | semidirect |
| 245. C2 | #11721117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6196 | 2 |
| C2×C4×#1084 | 2 |
| C2×C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×#88449 | 2 |
| #11721117 | 2 |
| C2×#63918 | 3 |