Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23765188 | C2 | semidirect |
| 5. #23764143 | C2 | semidirect |
| 6. #23761506 | C2 | semidirect |
| 7. C79×#1377 | C2 | semidirect |
| 21. #19098374 | C4 | semidirect |
| 54. #14579093 | C2×C4 | semidirect |
| 66. M32×C79 | C2×C4 | semidirect |
| 84. Dic316 | C4⋊C4 | semidirect |
| 88. D632 | C4⋊C4 | semidirect |
| 188. #1377 | D79 | semidirect |
| 189. C79 | #12943 | semidirect |
| 236. M32 | C4×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772202 | 2 |
| #23765188 | 2 |
| C2×#19098374 | 2 |
| #23765113 | 2 |
| #23764143 | 2 |
| #23761506 | 2 |
| C79×#1377 | 2 |
| #12943 | 79 |