Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
274 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 2. #23765718 | C2 | semidirect |
| 3. C2×#19098403 | C2 | semidirect |
| 4. #23761592 | C2 | semidirect |
| 5. #23761583 | C2 | semidirect |
| 6. #23761542 | C2 | semidirect |
| 7. C79×#2222 | C2 | semidirect |
| 120. #2222 | D79 | semidirect |
| 124. C79 | #13672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776553 | 2 |
| #23765718 | 2 |
| C2×#19098403 | 2 |
| #23761592 | 2 |
| #23761583 | 2 |
| #23761542 | 2 |
| C79×#2222 | 2 |
| #13672 | 79 |