Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765302 | C2 | semidirect |
| 4. #23761463 | C2 | semidirect |
| 5. #23761380 | C2 | semidirect |
| 6. #23761316 | C2 | semidirect |
| 55. C79⋊C16 | SD16 | semidirect |
| 80. Dic158 | M32 | semidirect |
| 113. C79 | #12050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765302 | 2 |
| #23765232 | 2 |
| C8×#11929612 | 2 |
| #23761463 | 2 |
| #23761380 | 2 |
| #23761316 | 2 |
| C79×D4⋊C16 | 2 |
| #12050 | 79 |