Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×D628 | C2 | semidirect |
| 3. C2×#19097693 | C2 | semidirect |
| 4. C2×#19097693 | C2 | semidirect |
| 5. #23757175 | C2 | semidirect |
| 6. #23757036 | C2 | semidirect |
| 7. #336×C157 | C2 | semidirect |
| 13. C2×D1256 | C4 | semidirect |
| 37. C2×D628 | C2×C4 | semidirect |
| 61. C2×C8×C157 | C2×C4 | semidirect |
| 85. D628 | C22⋊C4 | semidirect |
| 99. C2×C4×C157 | D8 | semidirect |
| 146. C157 | #1879 | semidirect |
| 154. #336 | D157 | semidirect |
| 201. C2×C8 | C4×D157 | semidirect |
| 246. C2×C4 | D1256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1256 | 2 |
| C2×C4×D628 | 2 |
| C2×#19097693 | 2 |
| #23757175 | 2 |
| #23757036 | 2 |
| #336×C157 | 2 |
| #1879 | 157 |