Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
606 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 606 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 |
|---|---|---|
| 3. #23764386 | C2 | semidirect |
| 5. #23761279 | C2 | semidirect |
| 6. #23761247 | C2 | semidirect |
| 7. C2×#328×C79 | C2 | semidirect |
| 11. #19098881 | C4 | semidirect |
| 14. #19098702 | C4 | semidirect |
| 58. C22⋊(C79⋊C8) | C2×C4 | semidirect |
| 63. C22×Q8×C79 | C2×C4 | semidirect |
| 72. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 108. C22⋊Dic79 | SD16 | semidirect |
| 255. C2×#328 | D79 | semidirect |
| 258. C79 | #9275 | semidirect |
| 282. C22×Q8 | C4×D79 | semidirect |
| 305. C2×C4⋊C4 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774153 | 2 |
| #23766447 | 2 |
| #23764386 | 2 |
| #23761969 | 2 |
| #23761279 | 2 |
| #23761247 | 2 |
| C2×#328×C79 | 2 |
| #9275 | 79 |