Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
406 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C11 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. C11×#97 | Q8 | semidirect |
| 25. #10583 | C11 | direct (N × H) |
| 81. #97 | Q8×C11 | semidirect |
| 103. C11 | #10583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2844 | 2 |
| C11×#1847 | 2 |
| C11×#1295 | 2 |
| #10583 | 11 |