Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
598 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 598 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 |
|---|---|---|
| 1. #23773518 | C2 | semidirect |
| 2. #23769261 | C2 | semidirect |
| 3. #23762024 | C2 | semidirect |
| 4. #23761947 | C2 | semidirect |
| 5. #23761848 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 220. C79 | #10020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773518 | 2 |
| #23769261 | 2 |
| #23762024 | 2 |
| #23761947 | 2 |
| #23761848 | 2 |
| #23761265 | 2 |
| C79×#3153 | 2 |
| #10020 | 79 |