Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 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 |
|---|---|---|
| 2. #31770962 | C2 | direct (N × H) |
| 3. C2×#22575376 | C2 | semidirect |
| 5. C2×C4×#14524130 | C2 | semidirect |
| 6. C2×#125×C269 | C2 | semidirect |
| 13. #22575376 | C22 | semidirect |
| 15. C4×#14524130 | C22 | semidirect |
| 17. #125×C269 | C22 | semidirect |
| 69. C2×C269 | #488 | semidirect |
| 73. C269 | C2×#488 | semidirect |
| 75. C2×#125 | D269 | semidirect |
| 85. #125 | C2×D269 | semidirect |
| 144. C2 | #31770962 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575441 | 2 |
| #31770962 | 2 |
| C2×#22575376 | 2 |
| C2×#22575373 | 2 |
| C2×C4×#14524130 | 2 |
| C2×#125×C269 | 2 |
| C2×#488 | 269 |