Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
616 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 616 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 |
|---|---|---|
| 1. C22×D2152 | C2 | semidirect |
| 2. C2×#22575427 | C2 | semidirect |
| 3. #31770841 | C2 | direct (N × H) |
| 4. C2×#22575387 | C2 | semidirect |
| 5. C2×#22575375 | C2 | semidirect |
| 6. C23×C8×C269 | C2 | semidirect |
| 10. C2×D2152 | C22 | semidirect |
| 12. #22575427 | C22 | semidirect |
| 15. #22575387 | C22 | semidirect |
| 16. #22575375 | C22 | semidirect |
| 21. C22×C8×C269 | C22 | semidirect |
| 43. C2×C8×C269 | D4 | semidirect |
| 58. C23×C269 | D8 | semidirect |
| 71. C8×C269 | C2×D4 | semidirect |
| 77. C22×C269 | C2×D8 | semidirect |
| 90. C2×C269 | #466 | semidirect |
| 95. C269 | C2×#466 | semidirect |
| 98. C23×C8 | D269 | semidirect |
| 111. C22×C8 | C2×D269 | semidirect |
| 136. C2×C8 | C22⋊D269 | semidirect |
| 148. C23 | D2152 | semidirect |
| 167. C8 | C2×C22⋊D269 | semidirect |
| 177. C22 | C2×D2152 | semidirect |
| 187. C2 | #31770841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2152 | 2 |
| C2×#22575427 | 2 |
| #31770841 | 2 |
| C2×#22575387 | 2 |
| C2×#22575375 | 2 |
| C23×C8×C269 | 2 |
| C2×#466 | 269 |