Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 2. #23765173 | C2 | semidirect |
| 5. #23764148 | C2 | semidirect |
| 6. #23761502 | C2 | semidirect |
| 7. C79×#1376 | C2 | semidirect |
| 21. #19098374 | C4 | semidirect |
| 46. #14579093 | C2×C4 | semidirect |
| 57. M32×C79 | C2×C4 | semidirect |
| 161. #1376 | D79 | semidirect |
| 162. C79 | #12951 | semidirect |
| 203. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579183 | 2 |
| #23765173 | 2 |
| #23765150 | 2 |
| #23765137 | 2 |
| #23764148 | 2 |
| #23761502 | 2 |
| C79×#1376 | 2 |
| #12951 | 79 |