Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #31771086 | C2 | semidirect |
| 3. C2×#22575381 | C2 | semidirect |
| 4. #31770610 | C2 | semidirect |
| 5. #31770374 | C2 | semidirect |
| 6. #31770365 | C2 | semidirect |
| 7. #390×C269 | C2 | semidirect |
| 10. #22575479 | C4 | semidirect |
| 42. #16864386 | C2×C4 | semidirect |
| 58. C2×D4×C269 | C2×C4 | semidirect |
| 69. Dic538 | C22⋊C4 | semidirect |
| 71. D1076 | C22⋊C4 | semidirect |
| 132. C269 | #1883 | semidirect |
| 138. #390 | D269 | semidirect |
| 174. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| #31771086 | 2 |
| C2×#22575381 | 2 |
| #31770610 | 2 |
| #31770374 | 2 |
| #31770365 | 2 |
| #390×C269 | 2 |
| #1883 | 269 |