Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
994 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 283 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. C2×#19098959 | C2 | semidirect |
| 4. #23762988 | C2 | direct (N × H) |
| 5. C2×C8×C79⋊C8 | C2 | semidirect |
| 6. C2×#498×C79 | C2 | semidirect |
| 12. #19098959 | C22 | semidirect |
| 19. C8×C79⋊C8 | C22 | semidirect |
| 22. #498×C79 | C22 | semidirect |
| 68. C2×C79⋊C8 | SD16 | semidirect |
| 78. C2×C8×C79 | SD16 | semidirect |
| 109. C8×C79 | C2×SD16 | semidirect |
| 110. C79⋊C8 | C2×SD16 | semidirect |
| 124. C2×C79 | #1705 | semidirect |
| 129. C2×#498 | D79 | semidirect |
| 134. C79 | C2×#1705 | semidirect |
| 143. #498 | C2×D79 | semidirect |
| 204. C2×C8 | #11929611 | semidirect |
| 238. C8 | C2×#11929611 | semidirect |
| 252. C2 | #23762988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098959 | 2 |
| C2×#19098937 | 2 |
| C2×#19098936 | 2 |
| #23762988 | 2 |
| C2×C8×C79⋊C8 | 2 |
| C2×#498×C79 | 2 |
| C2×#1705 | 79 |