Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
334 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 82 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C11 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C8×C11 ◁ C22×C11×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C11×D16 | C2 | semidirect |
| 2. C2×C11×D32 | C2 | semidirect |
| 3. C11×#2215 | C2 | semidirect |
| 4. C11×#1415 | C2 | semidirect |
| 5. C11×C22⋊C32 | C2 | semidirect |
| 10. C2×C11×D16 | C22 | semidirect |
| 14. C2×C11×C32 | C22 | semidirect |
| 15. C11×#366 | C22 | semidirect |
| 28. C11×D16 | D4 | semidirect |
| 35. #13661 | C11 | direct (N × H) |
| 57. C22×D16 | C2×C11 | semidirect |
| 58. C2×D32 | C2×C11 | semidirect |
| 59. #2215 | C2×C11 | semidirect |
| 60. #1415 | C2×C11 | semidirect |
| 61. C22⋊C32 | C2×C11 | semidirect |
| 86. C2×D16 | C22×C11 | semidirect |
| 90. C2×C32 | C22×C11 | semidirect |
| 91. #366 | C22×C11 | semidirect |
| 102. C22×C11 | D32 | semidirect |
| 119. D16 | D4×C11 | semidirect |
| 153. C11 | #13661 | direct (N × H) |
| 183. C22 | C11×D32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×D16 | 2 |
| C2×C11×D32 | 2 |
| C11×#2215 | 2 |
| C11×#1415 | 2 |
| C11×C22⋊C32 | 2 |
| #13661 | 11 |