Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
928 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 69. C33×C4 | Q16 | semidirect |
| 153. C32×C4 | Dic12 | semidirect |
| 154. C32×C4 | #216 | semidirect |
| 172. C33 | #462 | semidirect |
| 231. C3×C4 | #3719 | semidirect |
| 232. C3×C4 | #3746 | semidirect |
| 245. C32 | #4849 | semidirect |
| 246. C32 | #5090 | semidirect |
| 272. C4 | #88800 | semidirect |
| 276. C3 | #10590388 | semidirect |
| 277. C3 | #10592548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C3×#64078 | 2 |
| C2×#88800 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722040 | 2 |
| #10592548 | 3 |
| #10590388 | 3 |