Finite Group DatabasebetaFinite Group DatabasebetaOrder 28928.
1106 conjugacy classes of subgroups.
The subgroup lattice has 250 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C113 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C113 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C113 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 116. C4×C113 | #401 | semidirect |
| 117. C4⋊#401 | C113 | direct (N × H) |
| 130. C113 | C4⋊#401 | direct (N × H) |
| 241. C4 | #401×C113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#401×C113 | 2 |
| C113×#1443 | 2 |
| C113×C4⋊#95 | 2 |
| C4×#95×C113 | 2 |
| C4⋊#401 | 113 |