Finite Group DatabasebetaFinite Group DatabasebetaOrder 3888.
578 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×A42 |
| commutator, socle, cosocle | C24×C32 | C33 |
| Fitting, prime radical | C24×C33 | C32 |
| hypercenter | C33 | A42 |
| hypocenter | C24 | #6896 |
| LCS | G ▷ C24×C32 ▷ C24 | |
| UCS | C1 ◁ C32 ◁ C33 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #13048081 | C3 | semidirect |
| 4. (C22⋊C9)⋊(C22⋊C9) | C3 | semidirect |
| 5. C22⋊C92 | C3 | semidirect |
| 35. C22×C22⋊C9 | 3−1+2 | semidirect |
| 94. C22⋊C9 | #1094 | semidirect |
| 117. C24 | #6896 | semidirect |
| 152. C22 | #11757844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#1094 | 3 |
| C32⋊(C22⋊(C22⋊C9)) | 3 |
| #13048081 | 3 |
| (C22⋊C9)⋊(C22⋊C9) | 3 |
| C22⋊C92 | 3 |
| #11757844 | 4 |