Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
311 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 59 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. #11720777 | C2 | semidirect |
| 4. #11720776 | C2 | semidirect |
| 64. #272 | #108 | semidirect |
| 94. H(3,𝔽3) | C2×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722445 | 2 |
| C2×C8×#272 | 2 |
| #11720777 | 2 |
| #11720776 | 2 |
| C2×C3×#108 | 9 |