Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
652 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #23761429 | C2 | direct (N × H) |
| 168. C2×C79 | #1354 | semidirect |
| 176. C79 | C2×#1354 | semidirect |
| 339. C2 | #23761429 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098483 | 2 |
| C2×#19098289 | 2 |
| #23761429 | 2 |
| C2×#343×C79 | 2 |
| C2×#1354 | 79 |