Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23774193 | C2 | semidirect |
| 2. #23765329 | C2 | semidirect |
| 3. #23765312 | C2 | semidirect |
| 4. #23761411 | C2 | semidirect |
| 5. #23761408 | C2 | semidirect |
| 6. #23761324 | C2 | semidirect |
| 7. C79×#1999 | C2 | semidirect |
| 28. C2×Dic316 | D4 | semidirect |
| 30. C2×D632 | D4 | semidirect |
| 44. #14579095 | D4 | semidirect |
| 45. #14579095 | D4 | semidirect |
| 205. #1999 | D79 | semidirect |
| 209. C79 | #12104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774193 | 2 |
| #23765329 | 2 |
| #23765312 | 2 |
| #23761411 | 2 |
| #23761408 | 2 |
| #23761324 | 2 |
| C79×#1999 | 2 |
| #12104 | 79 |