Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. C4×#16864402 | C2 | semidirect |
| 3. #31770621 | C2 | semidirect |
| 4. #31770579 | C2 | semidirect |
| 5. #31770376 | C2 | semidirect |
| 6. #31770365 | C2 | semidirect |
| 7. C2×#104×C269 | C2 | semidirect |
| 9. #22575484 | C4 | semidirect |
| 11. #22575479 | C4 | semidirect |
| 43. #16864386 | C2×C4 | semidirect |
| 58. C2×Q8×C269 | C2×C4 | semidirect |
| 60. C2×D4×C269 | C2×C4 | semidirect |
| 129. C269 | #1906 | semidirect |
| 134. C2×#104 | D269 | semidirect |
| 168. C2×Q8 | C4×D269 | semidirect |
| 172. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771403 | 2 |
| C4×#16864402 | 2 |
| #31770621 | 2 |
| #31770579 | 2 |
| #31770376 | 2 |
| #31770365 | 2 |
| C2×#104×C269 | 2 |
| #1906 | 269 |