Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1018 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 103 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. #23774158 | C2 | semidirect |
| 2. C2×#19098714 | C2 | semidirect |
| 4. #23764384 | C2 | semidirect |
| 5. #23761967 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C79×#1786 | C2 | semidirect |
| 31. C22×Dic158 | D4 | semidirect |
| 51. C2×C4⋊Dic79 | D4 | semidirect |
| 63. C22⋊(C79⋊C8) | D4 | semidirect |
| 74. C22×C8×C79 | D4 | semidirect |
| 113. C22⋊Dic79 | SD16 | semidirect |
| 261. #1786 | D79 | semidirect |
| 264. C79 | #9954 | semidirect |
| 305. C22×C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774158 | 2 |
| C2×#19098714 | 2 |
| #23767033 | 2 |
| #23764384 | 2 |
| #23761967 | 2 |
| #23761247 | 2 |
| C79×#1786 | 2 |
| #9954 | 79 |