Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
694 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23772441 | C2 | semidirect |
| 2. #23761791 | C2 | semidirect |
| 3. #23761721 | C2 | semidirect |
| 4. #23761233 | C2 | semidirect |
| 23. C4⋊(C79⋊C8) | D4 | semidirect |
| 68. C2×D4×C79 | M16 | semidirect |
| 93. C42×C79 | M16 | semidirect |
| 174. C79 | #8963 | semidirect |
| 234. C2×D4 | #11929608 | semidirect |
| 262. C42 | #11929608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772441 | 2 |
| #23761791 | 2 |
| #23761721 | 2 |
| #23761233 | 2 |
| C4×#127×C79 | 2 |
| #8963 | 79 |