Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23762436 | C2 | semidirect |
| 3. #23761427 | C2 | semidirect |
| 4. #23761332 | C2 | semidirect |
| 5. C79×#2804 | C2 | semidirect |
| 151. #2804 | D79 | semidirect |
| 156. C79 | #12127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764441 | 2 |
| #23762436 | 2 |
| #23761427 | 2 |
| #23761332 | 2 |
| C79×#2804 | 2 |
| #12127 | 79 |