Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. #23764243 | C2 | semidirect |
| 4. #23762086 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 7. C79×#1309 | C2 | semidirect |
| 141. D316 | #101 | semidirect |
| 189. #1309 | D79 | semidirect |
| 191. C79 | #9357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773216 | 2 |
| #23772526 | 2 |
| #23764243 | 2 |
| #23762086 | 2 |
| #23761837 | 2 |
| #23761289 | 2 |
| C79×#1309 | 2 |
| #9357 | 79 |