Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
1504 conjugacy classes of subgroups; only the 821 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 821 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×#22575461 | C2 | direct (N × H) |
| 3. C22×#16864385 | C2 | semidirect |
| 4. C23×#14524130 | C2 | semidirect |
| 5. C22×C8×D269 | C2 | semidirect |
| 6. C22×M16×C269 | C2 | semidirect |
| 13. #22575461 | C22 | direct (N × H) |
| 14. C2×#16864385 | C22 | semidirect |
| 17. C22×#14524130 | C22 | semidirect |
| 18. C2×C8×D269 | C22 | semidirect |
| 20. C2×M16×C269 | C22 | semidirect |
| 31. #16864385 | C23 | semidirect |
| 34. C2×#14524130 | C23 | semidirect |
| 35. C8×D269 | C23 | semidirect |
| 41. M16×C269 | C23 | semidirect |
| 63. C22×C269 | #131 | semidirect |
| 73. C2×C269 | C2×#131 | semidirect |
| 76. C269 | C22×#131 | semidirect |
| 81. C22×M16 | D269 | semidirect |
| 93. C2×M16 | C2×D269 | semidirect |
| 114. M16 | C22×D269 | semidirect |
| 142. C22 | #22575461 | direct (N × H) |
| 151. C2 | C2×#22575461 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864402 | 2 |
| C2×#22575461 | 2 |
| C22×#16864385 | 2 |
| C23×#14524130 | 2 |
| C22×C8×D269 | 2 |
| C22×M16×C269 | 2 |
| C22×#131 | 269 |