Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #13077204 | C2 | semidirect |
| 3. #13070333 | C2 | semidirect |
| 4. #13070331 | C2 | semidirect |
| 5. C2×#10622152 | C2 | semidirect |
| 6. #13066723 | C2 | semidirect |
| 7. C11×#1386 | C2 | semidirect |
| 21. #10622478 | C4 | semidirect |
| 40. C2×D88 | C2×C4 | semidirect |
| 58. C11×#107 | D4 | semidirect |
| 61. C11×#106 | C2×C4 | semidirect |
| 62. #66882 | D4 | semidirect |
| 128. #1386 | D11 | semidirect |
| 243. #107 | D44 | semidirect |
| 248. #106 | C4×D11 | semidirect |
| 307. C11 | #12999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622478 | 2 |
| #13077204 | 2 |
| #13070333 | 2 |
| #13070331 | 2 |
| C2×#10622152 | 2 |
| #13066723 | 2 |
| C11×#1386 | 2 |
| #12999 | 11 |