Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23765625 | C2 | semidirect |
| 2. #23765624 | C2 | semidirect |
| 3. #23765623 | C2 | semidirect |
| 4. #23763017 | C2 | semidirect |
| 6. C16×C79⋊C8 | C2 | semidirect |
| 7. C79×#2240 | C2 | semidirect |
| 113. #2240 | D79 | semidirect |
| 117. C79 | #12509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765625 | 2 |
| #23765624 | 2 |
| #23765623 | 2 |
| #23763017 | 2 |
| #23763014 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#2240 | 2 |
| #12509 | 79 |