Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
574 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #23761847 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#2276 | C2 | semidirect |
| 10. #19098858 | C4 | semidirect |
| 11. #19098763 | C4 | semidirect |
| 121. Q8×C79 | #104 | semidirect |
| 185. #2276 | D79 | semidirect |
| 191. C79 | #9326 | semidirect |
| 306. Q8 | #14579089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773522 | 2 |
| #23764318 | 2 |
| #23761907 | 2 |
| #23761847 | 2 |
| #23761293 | 2 |
| #23761256 | 2 |
| C79×#2276 | 2 |
| #9326 | 79 |