Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
674 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23769763 | C2 | semidirect |
| 2. #23764631 | C2 | semidirect |
| 3. #23764471 | C2 | semidirect |
| 4. #23761222 | C2 | semidirect |
| 5. #23761221 | C2 | semidirect |
| 6. #23761220 | C2 | semidirect |
| 7. C79×#2011 | C2 | semidirect |
| 73. C2×D316 | D8 | semidirect |
| 96. C4⋊Dic79 | D8 | semidirect |
| 265. #2011 | D79 | semidirect |
| 269. C79 | #7737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769763 | 2 |
| #23764631 | 2 |
| #23764471 | 2 |
| #23761222 | 2 |
| #23761221 | 2 |
| #23761220 | 2 |
| C79×#2011 | 2 |
| #7737 | 79 |