Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic538 | C2 | semidirect |
| 2. #31770916 | C2 | semidirect |
| 3. #31770897 | C2 | semidirect |
| 4. #31770802 | C2 | semidirect |
| 5. #31770743 | C2 | semidirect |
| 6. #31770705 | C2 | semidirect |
| 7. #31770662 | C2 | semidirect |
| 66. Dic538 | #41 | semidirect |
| 111. C269 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic538 | 2 |
| #31770916 | 2 |
| #31770897 | 2 |
| #31770802 | 2 |
| #31770743 | 2 |
| #31770705 | 2 |
| #31770662 | 2 |
| #532×C269 | 2 |
| #3112 | 269 |