Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #23771988 | C2 | semidirect |
| 3. #23765136 | C2 | semidirect |
| 4. C2×#19098344 | C2 | semidirect |
| 5. #23761502 | C2 | semidirect |
| 6. #23761501 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 12. #19098818 | C4 | semidirect |
| 13. #19098813 | C4 | semidirect |
| 54. #14579093 | C2×C4 | semidirect |
| 55. #14579093 | D4 | semidirect |
| 64. C2×Q16×C79 | C2×C4 | semidirect |
| 66. C2×D8×C79 | C2×C4 | semidirect |
| 73. #106×C79 | D4 | semidirect |
| 196. #2145 | D79 | semidirect |
| 200. C79 | #13008 | semidirect |
| 226. C2×Q16 | C4×D79 | semidirect |
| 228. C2×D8 | C4×D79 | semidirect |
| 264. #106 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773005 | 2 |
| #23771988 | 2 |
| #23765136 | 2 |
| C2×#19098344 | 2 |
| #23761502 | 2 |
| #23761501 | 2 |
| C79×#2145 | 2 |
| #13008 | 79 |