Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
840 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #23765752 | C2 | semidirect |
| 3. #23761916 | C2 | semidirect |
| 4. #23761726 | C2 | semidirect |
| 5. #23761286 | C2 | semidirect |
| 6. #23761285 | C2 | semidirect |
| 7. C79×#1507 | C2 | semidirect |
| 13. #19098498 | C4 | semidirect |
| 14. #19098471 | C4 | semidirect |
| 53. C79⋊#95 | C2×C4 | semidirect |
| 54. C79⋊#95 | D4 | semidirect |
| 56. C22×D4×C79 | C2×C4 | semidirect |
| 63. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 69. #95×C79 | D4 | semidirect |
| 232. #1507 | D79 | semidirect |
| 236. C79 | #9409 | semidirect |
| 259. C22×D4 | C4×D79 | semidirect |
| 272. C2×C4⋊C4 | C4×D79 | semidirect |
| 298. #95 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768332 | 2 |
| #23765752 | 2 |
| #23761916 | 2 |
| #23761726 | 2 |
| #23761286 | 2 |
| #23761285 | 2 |
| C79×#1507 | 2 |
| #9409 | 79 |