Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. #31771259 | C2 | semidirect |
| 2. #31771001 | C2 | semidirect |
| 3. #31770929 | C2 | semidirect |
| 4. #31770921 | C2 | semidirect |
| 5. #31770892 | C2 | semidirect |
| 6. #31770885 | C2 | semidirect |
| 7. #31770856 | C2 | semidirect |
| 8. C4×#16864387 | C2 | semidirect |
| 9. #31770683 | C2 | semidirect |
| 10. #31770648 | C2 | semidirect |
| 11. #555×C269 | C2 | semidirect |
| 85. #14524130 | #41 | semidirect |
| 127. C269 | #3354 | semidirect |
| 129. #555 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771259 | 2 |
| #31771001 | 2 |
| #31770929 | 2 |
| #31770921 | 2 |
| #31770892 | 2 |
| #31770885 | 2 |
| #31770856 | 2 |
| C4×#16864387 | 2 |
| #31770683 | 2 |
| #31770648 | 2 |
| #555×C269 | 2 |
| #3354 | 269 |