Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22575500 | C2 | semidirect |
| 2. #31771403 | C2 | semidirect |
| 3. #31771176 | C2 | semidirect |
| 4. #31770786 | C2 | semidirect |
| 5. #31770776 | C2 | semidirect |
| 6. #31770622 | C2 | semidirect |
| 7. #31770621 | C2 | semidirect |
| 8. C2×#22575371 | C2 | semidirect |
| 9. #575×C269 | C2 | semidirect |
| 21. #22575484 | C22 | semidirect |
| 23. #22575479 | C22 | semidirect |
| 27. #22575451 | C22 | semidirect |
| 28. #22575440 | C22 | semidirect |
| 32. #22575380 | C22 | semidirect |
| 33. #22575379 | C22 | semidirect |
| 34. #22575371 | C22 | semidirect |
| 38. #137×C269 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C269 | C22 | semidirect |
| 185. C269 | #3020 | semidirect |
| 189. #575 | D269 | semidirect |
| 212. #137 | C2×D269 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575500 | 2 |
| #31771403 | 2 |
| #31771176 | 2 |
| #31770786 | 2 |
| #31770776 | 2 |
| #31770622 | 2 |
| #31770621 | 2 |
| C2×#22575371 | 2 |
| #575×C269 | 2 |
| #3020 | 269 |