Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
602 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 151 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. #23773980 | C2 | semidirect |
| 2. #23773977 | C2 | semidirect |
| 3. #23765673 | C2 | semidirect |
| 4. #23765649 | C2 | semidirect |
| 5. #23765624 | C2 | semidirect |
| 6. #23765485 | C2 | semidirect |
| 7. #23765244 | C2 | semidirect |
| 8. C4×C16×D79 | C2 | semidirect |
| 9. C79×#2240 | C2 | semidirect |
| 102. C79⋊C16 | #41 | semidirect |
| 142. C4×D79 | D16 | semidirect |
| 179. #2240 | D79 | semidirect |
| 183. C79 | #33733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773980 | 2 |
| #23773977 | 2 |
| #23765673 | 2 |
| #23765649 | 2 |
| #23765624 | 2 |
| #23765485 | 2 |
| #23765244 | 2 |
| C4×C16×D79 | 2 |
| C79×#2240 | 2 |
| #33733 | 79 |