Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31771010 | C2 | semidirect |
| 2. #31770977 | C2 | semidirect |
| 3. #31770951 | C2 | semidirect |
| 4. C8×#14524130 | C2 | semidirect |
| 30. #14524130 | D8 | semidirect |
| 38. C8×C269 | SD16 | semidirect |
| 51. C269 | #1706 | semidirect |
| 90. C8 | #16864390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771010 | 2 |
| #31770977 | 2 |
| #31770951 | 2 |
| C8×#14524130 | 2 |
| #493×C269 | 2 |
| #1706 | 269 |