Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26020426 | C2 | semidirect |
| 3. #26019022 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#1570 | C2 | semidirect |
| 138. #1570 | D89 | semidirect |
| 142. C89 | #10661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021049 | 2 |
| #26020426 | 2 |
| #26019022 | 2 |
| #26018678 | 2 |
| #26018676 | 2 |
| #26018082 | 2 |
| C89×#1570 | 2 |
| #10661 | 89 |