Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22575452 | C2 | semidirect |
| 3. #31770884 | C2 | direct (N × H) |
| 4. C2×#22575386 | C2 | semidirect |
| 5. C2×#22575382 | C2 | semidirect |
| 8. C2×#107×C269 | C2 | semidirect |
| 14. #22575452 | C22 | semidirect |
| 21. #22575386 | C22 | semidirect |
| 22. #22575382 | C22 | semidirect |
| 28. #107×C269 | C22 | semidirect |
| 34. C2×D1076 | Q8 | semidirect |
| 65. D1076 | C2×Q8 | semidirect |
| 100. C2×C269 | #474 | semidirect |
| 105. C269 | C2×#474 | semidirect |
| 111. C2×#107 | D269 | semidirect |
| 131. #107 | C2×D269 | semidirect |
| 207. C2 | #31770884 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575452 | 2 |
| C2×#22575415 | 2 |
| #31770884 | 2 |
| C2×#22575386 | 2 |
| C2×#22575382 | 2 |
| C2×#22575375 | 2 |
| C2×#22575373 | 2 |
| C2×#107×C269 | 2 |
| C2×#474 | 269 |