Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
615 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 615 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. #10619900 | C3 | direct (N × H) |
| 18. C32×H(3,𝔽3) | Q8 | semidirect |
| 61. C34 | Dic6 | semidirect |
| 69. C3×H(3,𝔽3) | Dic6 | semidirect |
| 70. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 148. C33 | #627 | semidirect |
| 149. C33 | C3×Dic6 | semidirect |
| 160. H(3,𝔽3) | C3×Dic6 | semidirect |
| 233. C32 | #6196 | semidirect |
| 235. C32 | C3×#627 | semidirect |
| 263. C3 | C3×#6196 | semidirect |
| 264. C3 | #10619900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1084 | 2 |
| C3×C3⋊((C3⋊Dic3)⋊C3) | 2 |
| C3×#6293 | 3 |
| #10619900 | 3 |
| C3×#6196 | 3 |