Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×Dic1076 | C2 | semidirect |
| 4. #31770881 | C2 | direct (N × H) |
| 5. C2×#22575371 | C2 | semidirect |
| 6. C2×#108×C269 | C2 | semidirect |
| 15. C2×Dic1076 | C22 | semidirect |
| 22. #22575371 | C22 | semidirect |
| 25. #108×C269 | C22 | semidirect |
| 100. C2×C269 | #473 | semidirect |
| 103. C269 | C2×#473 | semidirect |
| 109. C2×#108 | D269 | semidirect |
| 128. #108 | C2×D269 | semidirect |
| 205. C2 | #31770881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C22×Dic1076 | 2 |
| C2×#22575459 | 2 |
| #31770881 | 2 |
| C2×#22575371 | 2 |
| C2×#108×C269 | 2 |
| C2×#473 | 269 |