Finite Group DatabasebetaFinite Group Databasebeta← C3⋊((C3⋊SL(2,ℤ/4))⋊C3) #13048413
Order 1296.
332 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 2. C3⋊(C3⋊SL(2,ℤ/4)) | C3 | semidirect |
| 5. C3×C22⋊H(3,𝔽3) | C4 | semidirect |
| 22. C22×C33 | Dic3 | semidirect |
| 24. C32×A4 | C3×C4 | semidirect |
| 29. C22⋊H(3,𝔽3) | Dic3 | semidirect |
| 70. C22×C32 | C3⋊Dic3 | semidirect |
| 74. C3×A4 | C3×Dic3 | semidirect |
| 85. C33 | SL(2,ℤ/4) | semidirect |
| 131. C22×C3 | (C3⋊Dic3)⋊C3 | semidirect |
| 149. C32 | C3⋊SL(2,ℤ/4) | semidirect |
| 171. C22 | C3⋊((C3⋊Dic3)⋊C3) | semidirect |
| 178. C3 | (C3⋊SL(2,ℤ/4))⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊H(3,𝔽3) | 2 |
| C3⋊(C3⋊SL(2,ℤ/4)) | 3 |
| C3×#3757 | 3 |
| (C3⋊SL(2,ℤ/4))⋊C3 | 3 |
| C3⋊((C3⋊Dic3)⋊C3) | 4 |