Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #23772037 | C2 | semidirect |
| 3. #23762068 | C2 | semidirect |
| 4. #23761712 | C2 | semidirect |
| 5. #23761260 | C2 | semidirect |
| 6. #23761259 | C2 | semidirect |
| 7. C79×#1545 | C2 | semidirect |
| 49. C4⋊(C79⋊C8) | D4 | semidirect |
| 68. C4⋊C8×C79 | D4 | semidirect |
| 220. #1545 | D79 | semidirect |
| 224. C79 | #9198 | semidirect |
| 278. C4⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772037 | 2 |
| #23769151 | 2 |
| #23762068 | 2 |
| #23761712 | 2 |
| #23761260 | 2 |
| #23761259 | 2 |
| C79×#1545 | 2 |
| #9198 | 79 |