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 |
|---|---|---|
| 1. C2×#22575445 | C2 | semidirect |
| 2. #31770959 | C2 | direct (N × H) |
| 3. C2×#22575377 | C2 | semidirect |
| 5. C2×C4×#14524130 | C2 | semidirect |
| 9. #22575445 | C22 | semidirect |
| 12. #22575377 | C22 | semidirect |
| 14. C4×#14524130 | C22 | semidirect |
| 70. C2×C269 | #488 | semidirect |
| 73. C269 | C2×#488 | semidirect |
| 144. C2 | #31770959 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575445 | 2 |
| #31770959 | 2 |
| C2×#22575377 | 2 |
| C2×#22575374 | 2 |
| C2×C4×#14524130 | 2 |
| C2×#124×C269 | 2 |
| C2×#488 | 269 |