Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 3. #31770648 | C2 | semidirect |
| 4. #31770645 | C2 | semidirect |
| 5. #31770641 | C2 | semidirect |
| 6. C2×#22575384 | C2 | semidirect |
| 8. #22575460 | C4 | semidirect |
| 26. #16864386 | C2×C4 | semidirect |
| 27. C2×#14524130 | C2×C4 | semidirect |
| 76. C269 | #2912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #31771088 | 2 |
| #31770648 | 2 |
| #31770645 | 2 |
| #31770641 | 2 |
| C2×#22575384 | 2 |
| #520×C269 | 2 |
| #2912 | 269 |