Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. C2×#22575461 | C2 | semidirect |
| 3. #31770726 | C2 | direct (N × H) |
| 4. C2×#22575379 | C2 | semidirect |
| 5. C2×#22575363 | C2 | semidirect |
| 6. C2×#108×C269 | C2 | semidirect |
| 8. #22575475 | C4 | semidirect |
| 10. C2×Dic1076 | C4 | semidirect |
| 11. C2×#16864391 | C4 | semidirect |
| 12. C2×D2152 | C4 | semidirect |
| 14. #22575461 | C22 | semidirect |
| 19. #22575379 | C22 | semidirect |
| 20. #22575363 | C22 | semidirect |
| 23. #108×C269 | C22 | semidirect |
| 33. Dic1076 | C2×C4 | semidirect |
| 34. #16864391 | C2×C4 | semidirect |
| 35. D2152 | C2×C4 | semidirect |
| 88. C2×C269 | #444 | semidirect |
| 91. C269 | C2×#444 | semidirect |
| 96. C2×#108 | D269 | semidirect |
| 113. #108 | C2×D269 | semidirect |
| 181. C2 | #31770726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| C2×#22575461 | 2 |
| #31770726 | 2 |
| C2×#22575379 | 2 |
| C2×#22575363 | 2 |
| C2×#108×C269 | 2 |
| C2×#444 | 269 |