Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
328 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #396 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#1574 | C2 | semidirect |
| 3. C11×#1309 | C2 | semidirect |
| 22. #10611 | C11 | direct (N × H) |
| 35. #1574 | C2×C11 | semidirect |
| 37. #1309 | C2×C11 | semidirect |
| 91. C11 | #10611 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#1574 | 2 |
| C11×#1545 | 2 |
| C11×#1309 | 2 |
| #10611 | 11 |