Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. #23762314 | C2 | semidirect |
| 2. #23762224 | C2 | semidirect |
| 3. #23761466 | C2 | semidirect |
| 4. #23761367 | C2 | semidirect |
| 5. #23761367 | C2 | semidirect |
| 6. #23761322 | C2 | semidirect |
| 58. D8×C79 | M16 | semidirect |
| 116. C79 | #12078 | semidirect |
| 160. D8 | #11929608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762314 | 2 |
| #23762224 | 2 |
| #23761466 | 2 |
| #23761367 | 2 |
| #23761322 | 2 |
| C79×#2177 | 2 |
| #12078 | 79 |