Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
652 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#22575410 | C2 | semidirect |
| 4. #31770501 | C2 | semidirect |
| 5. #31770494 | C2 | semidirect |
| 6. C4×#16864379 | C2 | semidirect |
| 7. C42×Dic269 | C2 | semidirect |
| 8. C4×C4⋊C4×C269 | C2 | semidirect |
| 11. C4×D1076 | C4 | semidirect |
| 44. C4×Dic269 | D4 | semidirect |
| 91. C4×C269 | #117 | semidirect |
| 102. C269 | #2293 | semidirect |
| 109. C4×C4⋊C4 | D269 | semidirect |
| 197. C4 | #22575410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1076 | 2 |
| C2×#22575410 | 2 |
| #31770506 | 2 |
| #31770501 | 2 |
| #31770494 | 2 |
| C4×#16864379 | 2 |
| C42×Dic269 | 2 |
| C4×C4⋊C4×C269 | 2 |
| #2293 | 269 |