Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23771353 | C2 | semidirect |
| 4. #23761225 | C2 | semidirect |
| 5. #23761223 | C2 | semidirect |
| 6. #23761222 | C2 | semidirect |
| 118. C4⋊C4×C79 | SD16 | semidirect |
| 217. C79 | #7747 | semidirect |
| 327. C4⋊C4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771353 | 2 |
| #23764631 | 2 |
| #23764488 | 2 |
| #23761225 | 2 |
| #23761223 | 2 |
| #23761222 | 2 |
| C79×#2041 | 2 |
| #7747 | 79 |