Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
544 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23772119 | C2 | semidirect |
| 3. #23762050 | C2 | semidirect |
| 4. #23761825 | C2 | semidirect |
| 5. #23761297 | C2 | semidirect |
| 6. #23761245 | C2 | semidirect |
| 7. C79×#1955 | C2 | semidirect |
| 117. C2×C8×C79 | D8 | semidirect |
| 210. #1955 | D79 | semidirect |
| 215. C79 | #9049 | semidirect |
| 321. C2×C8 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773400 | 2 |
| #23772119 | 2 |
| #23762050 | 2 |
| #23761825 | 2 |
| #23761297 | 2 |
| #23761245 | 2 |
| C79×#1955 | 2 |
| #9049 | 79 |