Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23764244 | C2 | semidirect |
| 3. #23762188 | C2 | semidirect |
| 5. #23762082 | C2 | semidirect |
| 7. C79×#1299 | C2 | semidirect |
| 165. #1299 | D79 | semidirect |
| 166. C79 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774327 | 2 |
| #23764244 | 2 |
| #23762188 | 2 |
| #23762133 | 2 |
| #23762082 | 2 |
| #23761818 | 2 |
| C79×#1299 | 2 |
| #10489 | 79 |