Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 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. #31771161 | C2 | direct (N × H) |
| 2. C2×#22575452 | C2 | semidirect |
| 3. C2×#22575445 | C2 | semidirect |
| 5. C2×#22575418 | C2 | semidirect |
| 8. C2×#125×C269 | C2 | semidirect |
| 12. #22575452 | C22 | semidirect |
| 13. #22575445 | C22 | semidirect |
| 15. #22575418 | C22 | semidirect |
| 25. #125×C269 | C22 | semidirect |
| 36. C2×C4×D269 | Q8 | semidirect |
| 63. C4×D269 | C2×Q8 | semidirect |
| 83. C2×C269 | #533 | semidirect |
| 87. C269 | C2×#533 | semidirect |
| 92. C2×#125 | D269 | semidirect |
| 102. #125 | C2×D269 | semidirect |
| 172. C2 | #31771161 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771161 | 2 |
| C2×#22575452 | 2 |
| C2×#22575445 | 2 |
| C2×#22575431 | 2 |
| C2×#22575418 | 2 |
| C2×#22575411 | 2 |
| C2×C42×D269 | 2 |
| C2×#125×C269 | 2 |
| C2×#533 | 269 |