Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 91 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. #23765673 | C2 | semidirect |
| 3. #23765625 | C2 | semidirect |
| 4. #23765623 | C2 | semidirect |
| 5. #23762992 | C2 | semidirect |
| 6. C8×C79⋊C16 | C2 | semidirect |
| 7. C79×#1706 | C2 | semidirect |
| 55. C79⋊C16 | SD16 | semidirect |
| 88. C8×C79 | D16 | semidirect |
| 115. #1706 | D79 | semidirect |
| 117. C79 | #12503 | semidirect |
| 198. C8 | #14579102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765673 | 2 |
| #23765649 | 2 |
| #23765625 | 2 |
| #23765623 | 2 |
| #23762992 | 2 |
| C8×C79⋊C16 | 2 |
| C79×#1706 | 2 |
| #12503 | 79 |