Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31770952 | C2 | semidirect |
| 3. #31770890 | C2 | semidirect |
| 4. #31770811 | C2 | semidirect |
| 5. #31770348 | C2 | semidirect |
| 6. #31770334 | C2 | semidirect |
| 7. Q8⋊C8×C269 | C2 | semidirect |
| 70. Q8×C269 | SD16 | semidirect |
| 99. C269 | #1642 | semidirect |
| 106. Q8⋊C8 | D269 | semidirect |
| 155. Q8 | #16864391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771277 | 2 |
| #31770952 | 2 |
| #31770890 | 2 |
| #31770811 | 2 |
| #31770348 | 2 |
| #31770334 | 2 |
| Q8⋊C8×C269 | 2 |
| #1642 | 269 |