Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
402 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 221 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. Q8×#14524130 | C2 | semidirect |
| 2. #31770683 | C2 | semidirect |
| 3. #31770662 | C2 | semidirect |
| 4. C4×#16864386 | C2 | semidirect |
| 36. #14524130 | #41 | semidirect |
| 38. Q8×C269 | M16 | semidirect |
| 63. C269 | #2971 | semidirect |
| 100. Q8 | #16864386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#14524130 | 2 |
| #31770683 | 2 |
| #31770662 | 2 |
| C4×#16864386 | 2 |
| C4×#41×C269 | 2 |
| #2971 | 269 |