Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 474 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 |
|---|---|---|
| 1. #23764441 | C2 | semidirect |
| 2. #23762436 | C2 | semidirect |
| 3. #23762334 | C2 | semidirect |
| 4. #23761427 | C2 | semidirect |
| 5. #23761403 | C2 | semidirect |
| 6. #23761332 | C2 | semidirect |
| 7. C79×#2828 | C2 | semidirect |
| 217. #2828 | D79 | semidirect |
| 224. C79 | #12198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764441 | 2 |
| #23762436 | 2 |
| #23762334 | 2 |
| #23761427 | 2 |
| #23761403 | 2 |
| #23761332 | 2 |
| C79×#2828 | 2 |
| #12198 | 79 |