Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
188 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23765693 | C2 | semidirect |
| 2. #23765517 | C2 | semidirect |
| 3. #23761604 | C2 | semidirect |
| 4. #23761590 | C2 | semidirect |
| 5. C2×D32×C79 | C2 | semidirect |
| 69. C2×D32 | D79 | semidirect |
| 74. C79 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765693 | 2 |
| #23765517 | 2 |
| #23761604 | 2 |
| #23761590 | 2 |
| C2×D32×C79 | 2 |
| #13700 | 79 |