Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22575475 | C2 | semidirect |
| 2. #31771276 | C2 | semidirect |
| 3. #31771260 | C2 | semidirect |
| 4. #31770978 | C2 | semidirect |
| 5. #31770834 | C2 | semidirect |
| 6. #31770816 | C2 | semidirect |
| 7. #31770801 | C2 | semidirect |
| 8. #31770769 | C2 | semidirect |
| 9. #31770752 | C2 | semidirect |
| 10. C4×#16864391 | C2 | semidirect |
| 11. C8×D4×C269 | C2 | semidirect |
| 61. #16864391 | D4 | semidirect |
| 127. C4×C269 | #135 | semidirect |
| 140. C269 | #3284 | semidirect |
| 152. C8×D4 | D269 | semidirect |
| 272. C4 | #22575475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| #31771276 | 2 |
| #31771260 | 2 |
| #31770978 | 2 |
| #31770834 | 2 |
| #31770816 | 2 |
| #31770801 | 2 |
| #31770769 | 2 |
| #31770752 | 2 |
| C4×#16864391 | 2 |
| C8×D4×C269 | 2 |
| #3284 | 269 |