Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#22575486 | C2 | semidirect |
| 2. C2×#22575461 | C2 | semidirect |
| 4. #31771181 | C2 | semidirect |
| 5. #31770864 | C2 | semidirect |
| 6. #31770852 | C2 | semidirect |
| 7. #31770847 | C2 | semidirect |
| 8. #31770835 | C2 | semidirect |
| 9. #31770599 | C2 | semidirect |
| 10. C2×#22575376 | C2 | semidirect |
| 11. #428×C269 | C2 | semidirect |
| 77. M16×C269 | D4 | semidirect |
| 143. C269 | #3063 | semidirect |
| 153. #428 | D269 | semidirect |
| 210. M16 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C2×#22575461 | 2 |
| #31771186 | 2 |
| #31771181 | 2 |
| #31770864 | 2 |
| #31770852 | 2 |
| #31770847 | 2 |
| #31770835 | 2 |
| #31770599 | 2 |
| C2×#22575376 | 2 |
| #428×C269 | 2 |
| #3063 | 269 |