Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 2. #31771009 | C2 | semidirect |
| 3. #31771006 | C2 | semidirect |
| 4. #31771005 | C2 | semidirect |
| 5. #31771002 | C2 | semidirect |
| 31. C2×#14524130 | Q8 | semidirect |
| 44. C2×C8×C269 | Q8 | semidirect |
| 78. C269 | #3160 | semidirect |
| 114. C2×C8 | Dic538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771158 | 2 |
| #31771009 | 2 |
| #31771006 | 2 |
| #31771005 | 2 |
| #31771002 | 2 |
| #31770643 | 2 |
| #31770641 | 2 |
| C2×C8×Dic269 | 2 |
| #427×C269 | 2 |
| #3160 | 269 |