Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#22575364 | C2 | semidirect |
| 4. C2×#22575363 | C2 | semidirect |
| 6. #31770359 | C2 | semidirect |
| 7. #336×C269 | C2 | semidirect |
| 13. C2×C8×D269 | C4 | semidirect |
| 16. #22575365 | C4 | semidirect |
| 68. #14524130 | C22⋊C4 | semidirect |
| 90. C2×D269 | #97 | semidirect |
| 104. C269 | #1752 | semidirect |
| 112. #336 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D269 | 2 |
| C2×#22575365 | 2 |
| C2×#22575364 | 2 |
| C2×#22575363 | 2 |
| C4×#16864379 | 2 |
| #31770359 | 2 |
| #336×C269 | 2 |
| #1752 | 269 |