Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #31771162 | C2 | semidirect |
| 2. #31770905 | C2 | semidirect |
| 3. #31770895 | C2 | semidirect |
| 4. #31770885 | C2 | semidirect |
| 5. #31770645 | C2 | semidirect |
| 6. #31770629 | C2 | semidirect |
| 10. #22575453 | C22 | semidirect |
| 11. #22575453 | C22 | semidirect |
| 12. #22575445 | C22 | semidirect |
| 18. #22575386 | C22 | semidirect |
| 19. #22575384 | C22 | semidirect |
| 20. C4⋊#14524130 | C22 | semidirect |
| 21. C4⋊#14524130 | C22 | semidirect |
| 48. C2×D4×C269 | Q8 | semidirect |
| 115. C269 | #3077 | semidirect |
| 154. C2×D4 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31770905 | 2 |
| #31770895 | 2 |
| #31770885 | 2 |
| #31770645 | 2 |
| #31770629 | 2 |
| #31770610 | 2 |
| C2×C4×D4×C269 | 2 |
| #3077 | 269 |