Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
760 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23761920 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761286 | C2 | semidirect |
| 7. C79×#1996 | C2 | semidirect |
| 9. C2×#14579192 | C4 | semidirect |
| 15. #19098562 | C4 | semidirect |
| 43. C2×#11929608 | C2×C4 | semidirect |
| 59. C22×Q8×C79 | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 229. #1996 | D79 | semidirect |
| 234. C79 | #9361 | semidirect |
| 262. C22×Q8 | C4×D79 | semidirect |
| 280. 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 |
|---|---|
| #23772658 | 2 |
| #23766228 | 2 |
| #23763345 | 2 |
| #23761920 | 2 |
| #23761306 | 2 |
| #23761286 | 2 |
| C79×#1996 | 2 |
| #9361 | 79 |