Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1018 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23774153 | C2 | semidirect |
| 3. #23764386 | C2 | semidirect |
| 4. #23763331 | C2 | semidirect |
| 5. #23761969 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 7. C2×#450×C79 | C2 | semidirect |
| 35. C22×C79⋊C8 | D4 | semidirect |
| 59. C22×Q8×C79 | D4 | semidirect |
| 76. C2×C4⋊C4×C79 | D4 | semidirect |
| 80. C22⋊C8×C79 | D4 | semidirect |
| 104. C22⋊Dic79 | SD16 | semidirect |
| 258. C2×#450 | D79 | semidirect |
| 264. C79 | #9954 | semidirect |
| 289. C22×Q8 | C22⋊D79 | semidirect |
| 320. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 335. C22⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| #23767033 | 2 |
| #23764386 | 2 |
| #23763331 | 2 |
| #23761969 | 2 |
| #23761246 | 2 |
| C2×#450×C79 | 2 |
| #9954 | 79 |