Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771333 | C2 | semidirect |
| 3. #31770956 | C2 | semidirect |
| 4. #31770954 | C2 | semidirect |
| 5. #31770890 | C2 | semidirect |
| 6. #31770889 | C2 | semidirect |
| 9. C8×Dic538 | C2 | semidirect |
| 78. Dic538 | SD16 | semidirect |
| 118. C269 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771333 | 2 |
| D4×Dic538 | 2 |
| #31770956 | 2 |
| #31770954 | 2 |
| #31770890 | 2 |
| #31770889 | 2 |
| #31770810 | 2 |
| #31770808 | 2 |
| C8×Dic538 | 2 |
| #31770696 | 2 |
| C4×SD16×C269 | 2 |
| #3359 | 269 |