Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 24. #16864392 | C8 | semidirect |
| 48. #14524130 | Q16 | semidirect |
| 71. C269 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14524130 | 2 |
| #31770729 | 2 |
| C4×#16864392 | 2 |
| #31770357 | 2 |
| #31770337 | 2 |
| C8×#14524130 | 2 |
| Q8⋊C8×C269 | 2 |
| C8×Q16 | 269 |