Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #31770729 | C2 | semidirect |
| 4. #31770335 | C2 | semidirect |
| 6. C8×#14524130 | C2 | semidirect |
| 7. #334×C269 | C2 | semidirect |
| 26. #16864391 | C8 | semidirect |
| 43. Dic538 | C2×C8 | semidirect |
| 53. #14524130 | SD16 | semidirect |
| 60. C8×C269 | C2×C8 | semidirect |
| 77. C269 | C8×SD16 | semidirect |
| 82. #334 | D269 | semidirect |
| 138. C8 | C8×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770729 | 2 |
| C4×#16864391 | 2 |
| #31770670 | 2 |
| #31770335 | 2 |
| #31770332 | 2 |
| C8×#14524130 | 2 |
| #334×C269 | 2 |
| C8×SD16 | 269 |