Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #31771162 | C2 | semidirect |
| 2. #31771001 | C2 | semidirect |
| 3. #31770977 | C2 | semidirect |
| 4. #31770957 | C2 | semidirect |
| 5. #31770951 | C2 | semidirect |
| 6. #31770832 | C2 | semidirect |
| 7. C4×#16864390 | C2 | semidirect |
| 8. C2×C4×#14524130 | C2 | semidirect |
| 72. #14524130 | #41 | semidirect |
| 84. C2×C4×C269 | SD16 | semidirect |
| 112. C269 | #3167 | semidirect |
| 195. C2×C4 | #16864390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31771001 | 2 |
| #31770977 | 2 |
| #31770957 | 2 |
| #31770951 | 2 |
| #31770832 | 2 |
| C4×#16864390 | 2 |
| C2×C4×#14524130 | 2 |
| #532×C269 | 2 |
| #3167 | 269 |