Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
238 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #23762285 | C2 | semidirect |
| 3. #23762284 | C2 | semidirect |
| 4. #23761471 | C2 | semidirect |
| 5. #23761362 | C2 | semidirect |
| 6. C16×C79⋊C8 | C2 | semidirect |
| 7. C79×#1331 | C2 | semidirect |
| 57. C79⋊C16 | M16 | semidirect |
| 91. C79⋊C8 | D16 | semidirect |
| 117. #1331 | D79 | semidirect |
| 119. C79 | #12081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579102 | 2 |
| #23762285 | 2 |
| #23762284 | 2 |
| #23761471 | 2 |
| #23761362 | 2 |
| C16×C79⋊C8 | 2 |
| C79×#1331 | 2 |
| #12081 | 79 |