Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23772423 | C2 | semidirect |
| 3. #23763389 | C2 | semidirect |
| 4. #23762069 | C2 | semidirect |
| 5. #23762067 | C2 | semidirect |
| 6. #23761303 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 50. C4⋊(C79⋊C8) | D4 | semidirect |
| 61. C4⋊C8×C79 | D4 | semidirect |
| 203. #1303 | D79 | semidirect |
| 204. C79 | #9397 | semidirect |
| 254. C4⋊C8 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772423 | 2 |
| #23768342 | 2 |
| #23763389 | 2 |
| #23762069 | 2 |
| #23762067 | 2 |
| #23761303 | 2 |
| C79×#1303 | 2 |
| #9397 | 79 |