Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1026 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23764199 | C2 | semidirect |
| 2. #23762095 | C2 | semidirect |
| 3. #23762011 | C2 | semidirect |
| 4. #23761741 | C2 | semidirect |
| 6. #19098620 | C22 | semidirect |
| 7. C2×C4⋊(C79⋊C8) | C22 | semidirect |
| 9. C2×#14579072 | C22 | semidirect |
| 174. C79 | #8456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764199 | 2 |
| #23762095 | 2 |
| #23762011 | 2 |
| #23761741 | 2 |
| C79×#3496 | 2 |
| #8456 | 79 |