Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31771079 | C2 | semidirect |
| 3. #31770621 | C2 | semidirect |
| 4. #31770611 | C2 | semidirect |
| 5. #31770578 | C2 | semidirect |
| 6. #31770362 | C2 | semidirect |
| 7. #344×C269 | C2 | semidirect |
| 12. C2×#16864391 | C4 | semidirect |
| 13. C2×D2152 | C4 | semidirect |
| 30. C2×Dic538 | C2×C4 | semidirect |
| 35. C2×D1076 | C2×C4 | semidirect |
| 56. C2×C8×C269 | C2×C4 | semidirect |
| 115. C269 | #1904 | semidirect |
| 122. #344 | D269 | semidirect |
| 165. 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×#22575481 | 2 |
| #31771079 | 2 |
| #31770621 | 2 |
| #31770611 | 2 |
| #31770578 | 2 |
| #31770362 | 2 |
| #344×C269 | 2 |
| #1904 | 269 |