Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
242 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #23761473 | C2 | semidirect |
| 5. #23761472 | C2 | semidirect |
| 6. #23761471 | C2 | semidirect |
| 7. C79×#1372 | C2 | semidirect |
| 28. #14579100 | C8 | semidirect |
| 59. C79⋊C16 | C2×C8 | semidirect |
| 66. C16×C79 | C2×C8 | semidirect |
| 109. #1372 | D79 | semidirect |
| 112. C79 | #12009 | semidirect |
| 171. C16 | C8×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579100 | 2 |
| #23762147 | 2 |
| #335×D79 | 2 |
| #23761473 | 2 |
| #23761472 | 2 |
| #23761471 | 2 |
| C79×#1372 | 2 |
| #12009 | 79 |