Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
602 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 151 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 |
|---|---|---|
| 24. C3×C3⋊(C3⋊C8) | Q8 | semidirect |
| 80. C3⋊(C3⋊C8) | Dic6 | semidirect |
| 130. C33 | #498 | semidirect |
| 195. C32 | #4680 | semidirect |
| 196. C32 | #5080 | semidirect |
| 221. C3 | #10590303 | semidirect |
| 222. C3 | #10590309 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #11722079 | 2 |
| #10590309 | 3 |
| #10590303 | 3 |