Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
592 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. #13079196 | C2 | semidirect |
| 2. #13079193 | C2 | semidirect |
| 3. #13070896 | C2 | semidirect |
| 4. #13070865 | C2 | semidirect |
| 5. #13070840 | C2 | semidirect |
| 6. #13070718 | C2 | semidirect |
| 7. #13070489 | C2 | semidirect |
| 8. C4×#66862 | C2 | semidirect |
| 9. C11×#2240 | C2 | semidirect |
| 115. C11⋊C16 | #41 | semidirect |
| 121. #2240 | D11 | semidirect |
| 288. C11 | #33748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079196 | 2 |
| #13079193 | 2 |
| #13070896 | 2 |
| #13070865 | 2 |
| #13070840 | 2 |
| #13070718 | 2 |
| #13070489 | 2 |
| C4×#66862 | 2 |
| C11×#2240 | 2 |
| #33748 | 11 |