Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#22575384 | C2 | semidirect |
| 5. #31770368 | C2 | semidirect |
| 6. #31770367 | C2 | semidirect |
| 7. C2×#106×C269 | C2 | semidirect |
| 18. #22575365 | C4 | semidirect |
| 39. C2×#14524130 | C2×C4 | semidirect |
| 51. C2×C8×C269 | C2×C4 | semidirect |
| 105. C2×D269 | #106 | semidirect |
| 123. C269 | #1853 | semidirect |
| 127. C2×#106 | D269 | semidirect |
| 169. C2×C8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D269 | 2 |
| C2×#22575384 | 2 |
| C2×#22575365 | 2 |
| #31770462 | 2 |
| #31770368 | 2 |
| #31770367 | 2 |
| C2×#106×C269 | 2 |
| #1853 | 269 |