Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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 |
|---|---|---|
| 3. #23763955 | C2 | semidirect |
| 4. #23763271 | C2 | semidirect |
| 6. C42×C79⋊C8 | C2 | semidirect |
| 7. C79×#1839 | C2 | semidirect |
| 76. C42×C79 | M16 | semidirect |
| 101. C79⋊C8 | #126 | semidirect |
| 123. #1839 | D79 | semidirect |
| 127. C79 | #21666 | semidirect |
| 196. C42 | #11929607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579155 | 2 |
| #23764004 | 2 |
| #23763955 | 2 |
| #23763271 | 2 |
| #23763180 | 2 |
| C42×C79⋊C8 | 2 |
| C79×#1839 | 2 |
| #21666 | 79 |