Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23774387 | C2 | semidirect |
| 2. #23773491 | C2 | semidirect |
| 3. #23764318 | C2 | semidirect |
| 4. #23761998 | C2 | semidirect |
| 5. #23761843 | C2 | semidirect |
| 6. #23761256 | C2 | semidirect |
| 7. C79×#2540 | C2 | semidirect |
| 38. #14579161 | D4 | semidirect |
| 39. #14579158 | D4 | semidirect |
| 47. C4⋊(C79⋊C8) | D4 | semidirect |
| 57. #14579072 | D4 | semidirect |
| 241. #2540 | D79 | semidirect |
| 246. C79 | #10004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774387 | 2 |
| #23773491 | 2 |
| #23764318 | 2 |
| #23761998 | 2 |
| #23761843 | 2 |
| #23761256 | 2 |
| C79×#2540 | 2 |
| #10004 | 79 |