Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23765649 | C2 | semidirect |
| 2. #23765219 | C2 | semidirect |
| 3. #23762756 | C2 | semidirect |
| 4. #23762752 | C2 | semidirect |
| 5. #23761471 | C2 | semidirect |
| 6. #23761447 | C2 | semidirect |
| 7. C79×#1361 | C2 | semidirect |
| 63. C79⋊C16 | D8 | semidirect |
| 93. D316 | D16 | semidirect |
| 131. #1361 | D79 | semidirect |
| 132. C79 | #12430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765649 | 2 |
| #23765219 | 2 |
| #23762756 | 2 |
| #23762752 | 2 |
| #23761471 | 2 |
| #23761447 | 2 |
| C79×#1361 | 2 |
| #12430 | 79 |