Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
314 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #340 |
| commutator | C2×C8 | C42×C11 |
| Frattini, cosocle | C23×C8 | C22×C11 |
| prime radical | C24×C11 | Q16 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 33. #7265 | C11 | direct (N × H) |
| 169. C11 | #7265 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2112 | 2 |
| C11×#1810 | 2 |
| C2×C11×#341 | 2 |
| #7265 | 11 |