Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23772521 | C2 | semidirect |
| 3. #23764240 | C2 | semidirect |
| 4. #23762067 | C2 | semidirect |
| 5. #23761840 | C2 | semidirect |
| 6. C79⋊#1309 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 159. D316 | #100 | semidirect |
| 209. #1299 | D79 | semidirect |
| 210. C79 | #9359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772881 | 2 |
| #23772521 | 2 |
| #23764240 | 2 |
| #23762067 | 2 |
| #23761840 | 2 |
| C79⋊#1309 | 2 |
| C79×#1299 | 2 |
| #9359 | 79 |