Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#16864390 | C2 | semidirect |
| 2. C2×#22575460 | C2 | semidirect |
| 3. #31771176 | C2 | semidirect |
| 4. #31770849 | C2 | semidirect |
| 5. #31770832 | C2 | semidirect |
| 6. #31770641 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 8. #31770610 | C2 | semidirect |
| 16. C2×#16864386 | C22 | semidirect |
| 18. C22×#14524130 | C22 | semidirect |
| 22. #22575432 | C22 | semidirect |
| 24. #22575386 | C22 | semidirect |
| 25. #22575384 | C22 | semidirect |
| 26. #22575376 | C22 | semidirect |
| 45. C2×#14524130 | D4 | semidirect |
| 120. C269 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864390 | 2 |
| C2×#22575460 | 2 |
| #31771176 | 2 |
| #31770849 | 2 |
| #31770832 | 2 |
| #31770641 | 2 |
| #31770613 | 2 |
| #31770610 | 2 |
| #535×C269 | 2 |
| #3057 | 269 |