Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
592 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 125 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×#22575378 | C2 | semidirect |
| 3. C2×#22575377 | C2 | semidirect |
| 4. C2×#22575376 | C2 | semidirect |
| 7. C2×#103×C269 | C2 | semidirect |
| 15. C2×Q8×D269 | C4 | semidirect |
| 87. Dic538 | C22⋊C4 | semidirect |
| 107. Q8×C269 | C22⋊C4 | semidirect |
| 134. C2×D269 | #103 | semidirect |
| 152. C269 | #1787 | semidirect |
| 158. C2×#103 | D269 | semidirect |
| 245. Q8 | #16864379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D269 | 2 |
| C2×#22575378 | 2 |
| C2×#22575377 | 2 |
| C2×#22575376 | 2 |
| C2×#22575365 | 2 |
| #31770462 | 2 |
| C2×#103×C269 | 2 |
| #1787 | 269 |