Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23765188 | C2 | semidirect |
| 5. #23764148 | C2 | semidirect |
| 6. #23761509 | C2 | semidirect |
| 7. C2×#364×C79 | C2 | semidirect |
| 148. C2×#364 | D79 | semidirect |
| 154. C79 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765188 | 2 |
| C2×#19098377 | 2 |
| #23765117 | 2 |
| #23764266 | 2 |
| #23764148 | 2 |
| #23761509 | 2 |
| C2×#364×C79 | 2 |
| #13478 | 79 |