Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
2078 conjugacy classes of subgroups.
The subgroup lattice has 216 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| socle, prime radical | C24×C11 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2402 | C2 | direct (N × H) |
| 45. C2×#2402 | C11 | direct (N × H) |
| 71. #2402 | C2×C11 | direct (N × H) |
| 148. C2×C11 | #2402 | direct (N × H) |
| 177. C11 | C2×#2402 | direct (N × H) |
| 211. C2 | C11×#2402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2402 | 2 |
| C2×C11×#400 | 2 |
| C2×C11×#398 | 2 |
| C2×C4×C11×C4⋊C4 | 2 |
| C2×C11×#376 | 2 |
| C2×#2402 | 11 |