Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23764345 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#1515 | C2 | semidirect |
| 9. #19098955 | C4 | semidirect |
| 10. #19098925 | C4 | semidirect |
| 56. #14579072 | C2×C4 | semidirect |
| 61. C4⋊Q8×C79 | C2×C4 | semidirect |
| 62. C4⋊Q8×C79 | C2×C4 | semidirect |
| 209. #1515 | D79 | semidirect |
| 212. C79 | #9379 | semidirect |
| 242. C4⋊Q8 | C4×D79 | semidirect |
| 243. C4⋊Q8 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774399 | 2 |
| #23766210 | 2 |
| #23764345 | 2 |
| #23761999 | 2 |
| #23761264 | 2 |
| #23761257 | 2 |
| C79×#1515 | 2 |
| #9379 | 79 |