Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
512 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#10622313 | C2 | semidirect |
| 3. C2×#10622154 | C2 | semidirect |
| 4. #13070329 | C2 | semidirect |
| 5. #13069482 | C2 | semidirect |
| 6. #13066725 | C2 | semidirect |
| 7. C11×#1376 | C2 | semidirect |
| 20. #10622521 | C4 | semidirect |
| 108. Dic44 | C22⋊C4 | semidirect |
| 114. D88 | C22⋊C4 | semidirect |
| 127. #1376 | D11 | semidirect |
| 305. C11 | #13029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622521 | 2 |
| C2×#10622313 | 2 |
| C2×#10622154 | 2 |
| #13070329 | 2 |
| #13069482 | 2 |
| #13066725 | 2 |
| C11×#1376 | 2 |
| #13029 | 11 |