Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
662 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23773864 | C2 | semidirect |
| 2. #23773492 | C2 | semidirect |
| 3. #23769253 | C2 | semidirect |
| 4. #23761948 | C2 | semidirect |
| 5. #23761842 | C2 | semidirect |
| 6. #23761266 | C2 | semidirect |
| 7. C79×#1533 | C2 | semidirect |
| 45. #14579161 | D4 | semidirect |
| 46. #14579158 | D4 | semidirect |
| 64. C4×C79⋊C8 | D4 | semidirect |
| 83. #97×C79 | D4 | semidirect |
| 231. #1533 | D79 | semidirect |
| 235. C79 | #10018 | semidirect |
| 306. #97 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773864 | 2 |
| #23773492 | 2 |
| #23769253 | 2 |
| #23761948 | 2 |
| #23761842 | 2 |
| #23761266 | 2 |
| C79×#1533 | 2 |
| #10018 | 79 |