Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23776534 | C2 | semidirect |
| 2. #23773120 | C2 | semidirect |
| 3. C2×#19098372 | C2 | semidirect |
| 4. #23765128 | C2 | semidirect |
| 5. #23765028 | C2 | semidirect |
| 6. #23761498 | C2 | semidirect |
| 7. C79×#3060 | C2 | semidirect |
| 43. C2×Dic316 | D4 | semidirect |
| 45. C2×D632 | D4 | semidirect |
| 56. C2×C79⋊C16 | D4 | semidirect |
| 58. #14579097 | D4 | semidirect |
| 229. #3060 | D79 | semidirect |
| 234. C79 | #13318 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776534 | 2 |
| #23773120 | 2 |
| C2×#19098372 | 2 |
| #23765128 | 2 |
| #23765028 | 2 |
| #23761498 | 2 |
| C79×#3060 | 2 |
| #13318 | 79 |