Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1316 conjugacy classes of subgroups; only the 415 normal subgroups are shown.
This group has 1316 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 |
|---|---|---|
| 38. C3⋊(C3⋊(C3⋊C8)) | Q8 | semidirect |
| 110. C33 | #446 | semidirect |
| 146. C32 | #4828 | semidirect |
| 171. C3 | #10592527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6308 | 2 |
| C33×C4⋊C8 | 2 |
| #11722185 | 2 |
| #11722184 | 2 |
| C8×C3⋊(C3⋊Dic3) | 2 |
| #11722173 | 2 |
| #10592527 | 3 |