Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031470 | C2 | semidirect |
| 2. C2×#19151968 | C2 | semidirect |
| 3. #26019586 | C2 | semidirect |
| 4. #26019580 | C2 | semidirect |
| 5. #26019575 | C2 | semidirect |
| 6. #26018879 | C2 | semidirect |
| 7. #26018872 | C2 | semidirect |
| 210. C89 | #19060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031470 | 2 |
| C2×#19151968 | 2 |
| #26019586 | 2 |
| #26019580 | 2 |
| #26019575 | 2 |
| #26018879 | 2 |
| #26018872 | 2 |
| C89×#3553 | 2 |
| #19060 | 89 |