Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 193 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. #31770501 | C2 | semidirect |
| 4. #31770469 | C2 | semidirect |
| 5. C4⋊C4×Dic269 | C2 | semidirect |
| 7. #31770450 | C2 | semidirect |
| 9. #22575412 | C4 | semidirect |
| 94. C269 | #2346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575412 | 2 |
| #31770501 | 2 |
| #31770499 | 2 |
| #31770469 | 2 |
| C4⋊C4×Dic269 | 2 |
| C4×C22⋊Dic269 | 2 |
| #31770450 | 2 |
| #380×C269 | 2 |
| #2346 | 269 |