Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #13070366 | C2 | semidirect |
| 3. C2×#10622201 | C2 | semidirect |
| 4. #13070343 | C2 | semidirect |
| 5. #13069407 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 7. C2×C11×#361 | C2 | semidirect |
| 59. C11×#108 | D4 | semidirect |
| 122. C2×#361 | D11 | semidirect |
| 233. #108 | C22⋊D11 | semidirect |
| 292. C11 | #13417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079097 | 2 |
| #13070366 | 2 |
| C2×#10622201 | 2 |
| #13070343 | 2 |
| #13069407 | 2 |
| #13066701 | 2 |
| C2×C11×#361 | 2 |
| #13417 | 11 |