Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
588 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23763386 | C2 | semidirect |
| 4. #23761524 | C2 | semidirect |
| 6. C2×D4×Dic79 | C4 | semidirect |
| 9. #19098466 | C4 | semidirect |
| 13. #19098429 | C4 | semidirect |
| 15. #19098409 | C4 | semidirect |
| 84. C2×D4×C79 | C4⋊C4 | semidirect |
| 94. C42×C79 | C4⋊C4 | semidirect |
| 182. C79 | #12799 | semidirect |
| 239. C2×D4 | Dic79⋊C4 | semidirect |
| 271. C42 | Dic79⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766126 | 2 |
| C2×#19098356 | 2 |
| #23763386 | 2 |
| #23761524 | 2 |
| C2×#353×C79 | 2 |
| #12799 | 79 |