Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
200 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 200 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 | C2×C8×C11 | C2×D4 |
| commutator | C2×C4 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle, prime radical | C22×C11 | C8×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C4×C11×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. #12061 | C11 | direct (N × H) |
| 112. C11 | #12061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2183 | 2 |
| C8×C11×Q16 | 2 |
| C11×#1367 | 2 |
| C11×Q8⋊C16 | 2 |
| C11×#1312 | 2 |
| #12061 | 11 |