Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
278 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 4. #11724103 | C2 | semidirect |
| 5. #11724102 | C2 | semidirect |
| 115. C33 | #483 | semidirect |
| 175. C32 | #5043 | semidirect |
| 211. C3 | #10596415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊PSU(3,𝔽2) | 2 |
| C2×#88940 | 2 |
| #11724243 | 2 |
| #11724103 | 2 |
| #11724102 | 2 |
| #10596415 | 3 |
| #5043 | 9 |