Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #31770563 | C2 | semidirect |
| 4. #31770560 | C2 | semidirect |
| 5. M16×Dic269 | C2 | semidirect |
| 6. C2×#22575363 | C2 | semidirect |
| 8. #22575460 | C4 | semidirect |
| 21. #131×C269 | C4 | semidirect |
| 25. #16864386 | C2×C4 | semidirect |
| 26. C2×#14524130 | C2×C4 | semidirect |
| 39. M16×C269 | C2×C4 | semidirect |
| 40. C2×C8×C269 | C2×C4 | semidirect |
| 68. C269 | #2875 | semidirect |
| 79. #131 | Dic269 | semidirect |
| 100. M16 | C2×Dic269 | semidirect |
| 104. C2×C8 | C2×Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575460 | 2 |
| #41×Dic269 | 2 |
| #31770563 | 2 |
| #31770560 | 2 |
| M16×Dic269 | 2 |
| C2×#22575363 | 2 |
| C2×#131×C269 | 2 |
| #2875 | 269 |