Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #31771083 | C2 | semidirect |
| 3. #31770614 | C2 | semidirect |
| 5. #31770376 | C2 | semidirect |
| 6. #31770362 | C2 | semidirect |
| 22. C2×Q16×C269 | C4 | semidirect |
| 23. C2×SD16×C269 | C4 | semidirect |
| 109. C269 | #1905 | semidirect |
| 122. C2×Q16 | Dic269 | semidirect |
| 123. C2×SD16 | Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771083 | 2 |
| #31770622 | 2 |
| #31770614 | 2 |
| #31770579 | 2 |
| #31770376 | 2 |
| #31770362 | 2 |
| C2×#137×C269 | 2 |
| #1905 | 269 |