Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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⋊#11929639 | C2 | semidirect |
| 4. (C2×#11929639)⋊C4 | C2 | semidirect |
| 15. C22⋊Dic317 | C4 | semidirect |
| 16. #19099551 | C4 | semidirect |
| 17. C22⋊C4×C317 | C4 | semidirect |
| 32. C2×Dic317 | C2×C4 | semidirect |
| 36. C2×C4×C317 | C2×C4 | semidirect |
| 38. C22×C317 | C4⋊C4 | semidirect |
| 44. C2×D317 | C4⋊C4 | semidirect |
| 61. C317 | #385 | semidirect |
| 79. C22⋊C4 | #11929639 | semidirect |
| 98. C2×C4 | C2×#11929639 | semidirect |
| 109. C22 | C4⋊#11929639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11929639 | 2 |
| C2×C4⋊#11929639 | 2 |
| C2×C22⋊#11929639 | 2 |
| (C2×#11929639)⋊C4 | 2 |
| C22⋊C4×D317 | 2 |
| #385 | 317 |