Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
626 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 199 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. #23764362 | C2 | semidirect |
| 3. #23763560 | C2 | semidirect |
| 4. C2×#19098284 | C2 | semidirect |
| 16. #492×C79 | C4 | semidirect |
| 101. C8×C79 | #102 | semidirect |
| 131. C79 | #9842 | semidirect |
| 136. #492 | Dic79 | semidirect |
| 228. C8 | #14579082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764362 | 2 |
| #23764207 | 2 |
| #23763560 | 2 |
| C2×#19098284 | 2 |
| C2×#492×C79 | 2 |
| #9842 | 79 |