Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
560 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 161 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×#22579839 | C2 | semidirect |
| 3. #31799942 | C2 | semidirect |
| 4. #31799939 | C2 | semidirect |
| 5. #31799934 | C2 | semidirect |
| 6. #31799929 | C2 | semidirect |
| 7. #31799927 | C2 | semidirect |
| 9. C4×C4⋊Dic277 | C2 | semidirect |
| 10. C4×#17984540 | C2 | semidirect |
| 11. C4×C22⋊C4×C277 | C2 | semidirect |
| 137. C277 | #2395 | semidirect |
| 149. C4×C22⋊C4 | D277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D277 | 2 |
| C2×#22579839 | 2 |
| #31799942 | 2 |
| #31799939 | 2 |
| #31799934 | 2 |
| #31799929 | 2 |
| #31799927 | 2 |
| #31799918 | 2 |
| C4×C4⋊Dic277 | 2 |
| C4×#17984540 | 2 |
| C4×C22⋊C4×C277 | 2 |
| #2395 | 277 |