Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #31771325 | C2 | semidirect |
| 2. #31770951 | C2 | semidirect |
| 3. #31770926 | C2 | semidirect |
| 4. #31770890 | C2 | semidirect |
| 5. #31770832 | C2 | semidirect |
| 6. #31770802 | C2 | semidirect |
| 7. #31770767 | C2 | semidirect |
| 8. C4×#16864392 | C2 | semidirect |
| 9. D4×#14524130 | C2 | semidirect |
| 10. #31770601 | C2 | semidirect |
| 127. C269 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771325 | 2 |
| #31770951 | 2 |
| #31770926 | 2 |
| #31770890 | 2 |
| #31770832 | 2 |
| #31770802 | 2 |
| #31770767 | 2 |
| C4×#16864392 | 2 |
| D4×#14524130 | 2 |
| #31770601 | 2 |
| #550×C269 | 2 |
| #3304 | 269 |