Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23761933 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761253 | C2 | semidirect |
| 7. C79×#1996 | C2 | semidirect |
| 10. #19098876 | C4 | semidirect |
| 13. #19098702 | C4 | semidirect |
| 55. C22⋊(C79⋊C8) | C2×C4 | semidirect |
| 61. C22×Q8×C79 | C2×C4 | semidirect |
| 69. C2×C4⋊C4×C79 | C2×C4 | semidirect |
| 232. #1996 | D79 | semidirect |
| 237. C79 | #9341 | semidirect |
| 261. C22×Q8 | C4×D79 | semidirect |
| 281. C2×C4⋊C4 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774202 | 2 |
| #23766554 | 2 |
| #23761933 | 2 |
| #23761915 | 2 |
| #23761306 | 2 |
| #23761253 | 2 |
| C79×#1996 | 2 |
| #9341 | 79 |