Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 1. #23772506 | C2 | semidirect |
| 2. #23762110 | C2 | semidirect |
| 5. C79⋊#1308 | C2 | semidirect |
| 6. #23761263 | C2 | semidirect |
| 161. C79 | #9334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772506 | 2 |
| #23762110 | 2 |
| #23762024 | 2 |
| #23761752 | 2 |
| C79⋊#1308 | 2 |
| #23761263 | 2 |
| C79×#3215 | 2 |
| #9334 | 79 |