Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3164 conjugacy classes of subgroups; only the 1115 normal subgroups are shown.
This group has 3164 conjugacy classes of subgroups — too many to draw. Only its 1115 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 |
|---|---|---|
| 6. #11723931 | C2 | direct (N × H) |
| 73. C2×C33 | #125 | semidirect |
| 102. C33 | C2×#125 | semidirect |
| 114. C2×C32 | #890 | semidirect |
| 137. C32 | C2×#890 | semidirect |
| 149. C2×C3 | #64099 | semidirect |
| 162. C3 | C2×#64099 | semidirect |
| 163. C2 | #11723931 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88857 | 2 |
| C2×C4×C3⋊(C3⋊Dic3) | 2 |
| #11723931 | 2 |
| C2×#64099 | 3 |