Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
634 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 634 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 |
|---|---|---|
| 1. #23772860 | C2 | semidirect |
| 2. #23764193 | C2 | semidirect |
| 3. #23761851 | C2 | semidirect |
| 4. #23761275 | C2 | semidirect |
| 5. C79×#3245 | C2 | semidirect |
| 57. C2×D316 | D8 | semidirect |
| 163. #3245 | D79 | semidirect |
| 168. C79 | #10254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772860 | 2 |
| #23764193 | 2 |
| #23761851 | 2 |
| #23761275 | 2 |
| C79×#3245 | 2 |
| #10254 | 79 |