Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
446 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 446 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 |
|---|---|---|
| 1. #23769572 | C2 | semidirect |
| 4. #23761307 | C2 | semidirect |
| 5. #23761285 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 52. C22×D4×C79 | Q8 | semidirect |
| 59. C2×C4⋊C4×C79 | Q8 | semidirect |
| 217. C79 | #10382 | semidirect |
| 239. C22×D4 | Dic158 | semidirect |
| 251. C2×C4⋊C4 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769572 | 2 |
| #23764237 | 2 |
| #23761916 | 2 |
| #23761307 | 2 |
| #23761285 | 2 |
| #23761252 | 2 |
| C79×#1510 | 2 |
| #10382 | 79 |