Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
822 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23774618 | C2 | semidirect |
| 2. C2×#19098933 | C2 | semidirect |
| 3. #23762734 | C2 | semidirect |
| 4. #23762728 | C2 | semidirect |
| 5. #23762723 | C2 | semidirect |
| 6. #23762027 | C2 | semidirect |
| 7. #23762020 | C2 | semidirect |
| 210. C79 | #19060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774618 | 2 |
| C2×#19098933 | 2 |
| #23762734 | 2 |
| #23762728 | 2 |
| #23762723 | 2 |
| #23762027 | 2 |
| #23762020 | 2 |
| C79×#3553 | 2 |
| #19060 | 79 |