Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
600 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×#19098620 | C2 | semidirect |
| 3. C2×#19098302 | C2 | semidirect |
| 4. #23761282 | C2 | semidirect |
| 5. C79×#1749 | C2 | semidirect |
| 45. #14579072 | D4 | semidirect |
| 210. #1749 | D79 | semidirect |
| 213. C79 | #9124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098620 | 2 |
| #23771701 | 2 |
| C2×#19098302 | 2 |
| #23761282 | 2 |
| C79×#1749 | 2 |
| #9124 | 79 |