Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1494 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1494 conjugacy classes of subgroups — too many to draw. Only its 310 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C22×C11×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C11×#131 | C2 | semidirect |
| 2. C2×C11×#466 | C2 | semidirect |
| 3. C11×#2615 | C2 | semidirect |
| 4. C11×#1895 | C2 | semidirect |
| 5. C11×#1808 | C2 | semidirect |
| 31. C22×C8×C11 | D4 | semidirect |
| 42. #32933 | C11 | direct (N × H) |
| 71. C22×#131 | C2×C11 | semidirect |
| 72. C2×#466 | C2×C11 | semidirect |
| 73. #2615 | C2×C11 | semidirect |
| 74. #1895 | C2×C11 | semidirect |
| 75. #1808 | C2×C11 | semidirect |
| 141. C22×C8 | D4×C11 | semidirect |
| 185. C11 | #32933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×#131 | 2 |
| C2×C11×#466 | 2 |
| C11×#2615 | 2 |
| C11×#1895 | 2 |
| C11×#1808 | 2 |
| #32933 | 11 |