Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
704 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 237 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 |
|---|---|---|
| 3. #31770503 | C2 | semidirect |
| 4. #31770476 | C2 | semidirect |
| 5. #31770471 | C2 | semidirect |
| 6. #31770464 | C2 | semidirect |
| 7. #95×D269 | C2 | semidirect |
| 8. C4×C4⋊C4×C269 | C2 | semidirect |
| 13. C4×D1076 | C4 | semidirect |
| 37. C2×C4×D269 | C2×C4 | semidirect |
| 39. C4⋊Dic269 | C2×C4 | semidirect |
| 42. #16864379 | C2×C4 | semidirect |
| 50. C42×C269 | C2×C4 | semidirect |
| 56. D1076 | C4⋊C4 | semidirect |
| 101. C269 | #2349 | semidirect |
| 109. C4×C4⋊C4 | D269 | semidirect |
| 152. C42 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1076 | 2 |
| #31770503 | 2 |
| #31770476 | 2 |
| #31770471 | 2 |
| #31770464 | 2 |
| #95×D269 | 2 |
| C4×C4⋊C4×C269 | 2 |
| #2349 | 269 |