Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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×#22575453 | C2 | semidirect |
| 3. #31770896 | C2 | direct (N × H) |
| 4. C2×#22575385 | C2 | semidirect |
| 6. C2×C4⋊C8×C269 | C2 | semidirect |
| 11. #22575453 | C22 | semidirect |
| 18. #22575385 | C22 | semidirect |
| 22. C4⋊C8×C269 | C22 | semidirect |
| 28. C2×D1076 | Q8 | semidirect |
| 54. D1076 | C2×Q8 | semidirect |
| 85. C2×C269 | #476 | semidirect |
| 90. C269 | C2×#476 | semidirect |
| 96. C2×C4⋊C8 | D269 | semidirect |
| 112. C4⋊C8 | C2×D269 | semidirect |
| 177. C2 | #31770896 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575453 | 2 |
| C2×C4×D1076 | 2 |
| #31770896 | 2 |
| C2×#22575385 | 2 |
| C2×#22575375 | 2 |
| C2×C4⋊C8×C269 | 2 |
| C2×#476 | 269 |