Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #23761681 | C2 | semidirect |
| 5. M16×C79⋊C8 | C2 | semidirect |
| 6. #23761289 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 154. #1299 | D79 | semidirect |
| 155. C79 | #8241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772111 | 2 |
| #23762060 | 2 |
| #23761991 | 2 |
| #23761681 | 2 |
| M16×C79⋊C8 | 2 |
| #23761289 | 2 |
| C79×#1299 | 2 |
| #8241 | 79 |