Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
894 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 894 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. #23768559 | C2 | semidirect |
| 3. #23763344 | C2 | semidirect |
| 4. #23761933 | C2 | semidirect |
| 5. #23761726 | C2 | semidirect |
| 6. #23761254 | C2 | semidirect |
| 7. C79×#3007 | C2 | semidirect |
| 50. C2×C4×Dic79 | D4 | semidirect |
| 66. C22×Q8×C79 | D4 | semidirect |
| 80. C2×C4⋊C4×C79 | D4 | semidirect |
| 85. C22⋊C8×C79 | D4 | semidirect |
| 274. #3007 | D79 | semidirect |
| 281. C79 | #9942 | semidirect |
| 314. C22×Q8 | C22⋊D79 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D79 | semidirect |
| 353. C22⋊C8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23768559 | 2 |
| #23766715 | 2 |
| #23763344 | 2 |
| #23761933 | 2 |
| #23761726 | 2 |
| #23761254 | 2 |
| C79×#3007 | 2 |
| #9942 | 79 |