Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 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. C22×D1268 | C2 | semidirect |
| 2. C2×#19099559 | C2 | semidirect |
| 3. #23778700 | C2 | semidirect |
| 4. C22⋊#14579261 | C2 | semidirect |
| 5. #121×C317 | C2 | semidirect |
| 11. C2×#14579261 | C22 | semidirect |
| 13. C2×D4×C317 | C22 | semidirect |
| 15. C4⋊C4×C317 | C22 | semidirect |
| 23. D1268 | D4 | semidirect |
| 38. C22×C317 | D8 | semidirect |
| 53. C317 | #447 | semidirect |
| 57. #121 | D317 | semidirect |
| 65. C2×D4 | C2×D317 | semidirect |
| 69. C4⋊C4 | C2×D317 | semidirect |
| 96. C22 | #19099559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1268 | 2 |
| C2×#19099559 | 2 |
| #23778700 | 2 |
| C22⋊#14579261 | 2 |
| #121×C317 | 2 |
| #447 | 317 |