Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23764217 | C2 | semidirect |
| 2. #23763569 | C2 | semidirect |
| 3. C2×#19098303 | C2 | semidirect |
| 4. #23761281 | C2 | semidirect |
| 31. #14579072 | D4 | semidirect |
| 155. C79 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764217 | 2 |
| #23763569 | 2 |
| C2×#19098303 | 2 |
| #23761281 | 2 |
| C79×#2819 | 2 |
| #10424 | 79 |