Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575481 | C2 | semidirect |
| 2. C2×#22575450 | C2 | semidirect |
| 3. C4×#16864402 | C2 | semidirect |
| 4. #31770806 | C2 | semidirect |
| 5. #31770801 | C2 | semidirect |
| 6. #31770611 | C2 | semidirect |
| 7. #423×C269 | C2 | semidirect |
| 12. C2×#16864391 | C22 | semidirect |
| 13. C2×D2152 | C22 | semidirect |
| 17. C4×Dic538 | C22 | semidirect |
| 18. C4×D1076 | C22 | semidirect |
| 23. #22575375 | C22 | semidirect |
| 26. C4⋊C8×C269 | C22 | semidirect |
| 29. #16864402 | D4 | semidirect |
| 62. Dic538 | C2×D4 | semidirect |
| 69. D1076 | C2×D4 | semidirect |
| 94. C4×C269 | AGL(1,ℤ/8) | semidirect |
| 104. C269 | #3038 | semidirect |
| 111. #423 | D269 | semidirect |
| 130. C4⋊C8 | C2×D269 | semidirect |
| 201. C4 | #22575481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| C2×#22575450 | 2 |
| C4×#16864402 | 2 |
| #31770806 | 2 |
| #31770801 | 2 |
| #31770611 | 2 |
| #423×C269 | 2 |
| #3038 | 269 |