Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#19098305 | C2 | semidirect |
| 5. #23761298 | C2 | semidirect |
| 6. #23761244 | C2 | semidirect |
| 7. C79×#1470 | C2 | semidirect |
| 198. #1470 | D79 | semidirect |
| 201. C79 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774568 | 2 |
| #23772389 | 2 |
| #23762021 | 2 |
| C2×#19098305 | 2 |
| #23761298 | 2 |
| #23761244 | 2 |
| C79×#1470 | 2 |
| #9266 | 79 |