Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #13077467 | C2 | semidirect |
| 3. #13070491 | C2 | semidirect |
| 4. #13070462 | C2 | semidirect |
| 5. #13070331 | C2 | semidirect |
| 6. #13070212 | C2 | semidirect |
| 7. C11×#2158 | C2 | semidirect |
| 15. C2×D176 | C4 | semidirect |
| 18. #10622485 | C22 | semidirect |
| 20. C11×#367 | C22 | semidirect |
| 21. C11×#366 | C22 | semidirect |
| 22. #10622140 | C22 | semidirect |
| 23. C16×Dic11 | C22 | semidirect |
| 24. #10622129 | C22 | semidirect |
| 32. C2×D88 | C2×C4 | semidirect |
| 37. C2×C11×C16 | C2×C4 | semidirect |
| 47. D176 | C2×C4 | semidirect |
| 48. D176 | C2×C4 | semidirect |
| 80. #2158 | D11 | semidirect |
| 113. #367 | C2×D11 | semidirect |
| 114. #366 | C2×D11 | semidirect |
| 145. C2×C16 | C4×D11 | semidirect |
| 183. C11 | #33456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D176 | 2 |
| #13077467 | 2 |
| #13070491 | 2 |
| #13070462 | 2 |
| #13070331 | 2 |
| #13070212 | 2 |
| C11×#2158 | 2 |
| #33456 | 11 |