Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1540 conjugacy classes of subgroups; only the 415 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 415 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 |
|---|---|---|
| 13. #88863 | C4 | semidirect |
| 62. C3⋊(C3⋊Dic3) | Q16 | semidirect |
| 115. C33 | C4×Q16 | semidirect |
| 153. C32 | #4790 | semidirect |
| 179. C3 | #10592489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊(C3⋊Dic3) | 2 |
| C2×#88863 | 2 |
| #11723928 | 2 |
| C33×#103 | 2 |
| #11722186 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722177 | 2 |
| #10592489 | 3 |