Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#16864390 | C2 | semidirect |
| 2. C22×#16864385 | C2 | semidirect |
| 3. C2×#22575433 | C2 | semidirect |
| 5. #31770850 | C2 | direct (N × H) |
| 6. C2×#22575386 | C2 | semidirect |
| 7. C2×#22575378 | C2 | semidirect |
| 8. C2×#102×C269 | C2 | semidirect |
| 13. C2×#16864390 | C22 | semidirect |
| 15. C2×#16864385 | C22 | semidirect |
| 18. #22575433 | C22 | semidirect |
| 25. #22575386 | C22 | semidirect |
| 26. #22575378 | C22 | semidirect |
| 30. #102×C269 | C22 | semidirect |
| 47. C2×#14524130 | D4 | semidirect |
| 82. #14524130 | C2×D4 | semidirect |
| 118. C2×C269 | #468 | semidirect |
| 123. C269 | C2×#468 | semidirect |
| 132. C2×#102 | D269 | semidirect |
| 154. #102 | C2×D269 | semidirect |
| 243. C2 | #31770850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864390 | 2 |
| C22×#16864385 | 2 |
| C2×#22575433 | 2 |
| C2×#22575424 | 2 |
| #31770850 | 2 |
| C2×#22575386 | 2 |
| C2×#22575378 | 2 |
| C2×#102×C269 | 2 |
| C2×#468 | 269 |