Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C11×C16 | C23 |
| commutator | C22 | C22×C11×C16 |
| Frattini, cosocle | C2×C16 | C23×C11 |
| socle, prime radical | C22×C11 | C22×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C11×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. C11×C32 | Q8 | semidirect |
| 25. #13660 | C11 | direct (N × H) |
| 78. C32 | Q8×C11 | semidirect |
| 94. C11 | #13660 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C11×C16 | 2 |
| C11×C4⋊C32 | 2 |
| C11×#1397 | 2 |
| C4×C11×C32 | 2 |
| #13660 | 11 |