Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
602 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23773340 | C2 | semidirect |
| 3. #23763477 | C2 | semidirect |
| 4. #23761930 | C2 | semidirect |
| 5. #23761929 | C2 | semidirect |
| 6. #23761309 | C2 | semidirect |
| 7. C79×#3094 | C2 | semidirect |
| 52. C22⋊(C79⋊C8) | D4 | semidirect |
| 71. C2×C4⋊C4×C79 | D4 | semidirect |
| 72. C2×C4⋊C4×C79 | D4 | semidirect |
| 81. C22⋊C8×C79 | D4 | semidirect |
| 229. #3094 | D79 | semidirect |
| 235. C79 | #9983 | semidirect |
| 283. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 284. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 304. C22⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773340 | 2 |
| #23771422 | 2 |
| #23763477 | 2 |
| #23761930 | 2 |
| #23761929 | 2 |
| #23761309 | 2 |
| C79×#3094 | 2 |
| #9983 | 79 |