Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
618 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26020240 | C2 | semidirect |
| 3. #26018821 | C2 | semidirect |
| 4. #26018132 | C2 | semidirect |
| 5. C89×#2973 | C2 | semidirect |
| 9. #19151528 | C4 | semidirect |
| 10. #19151523 | C4 | semidirect |
| 11. #19151515 | C4 | semidirect |
| 12. #19151507 | C4 | semidirect |
| 62. C22⋊C8×C89 | D4 | semidirect |
| 216. #2973 | D89 | semidirect |
| 221. C89 | #9386 | semidirect |
| 272. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025208 | 2 |
| #26020240 | 2 |
| #26018821 | 2 |
| #26018132 | 2 |
| C89×#2973 | 2 |
| #9386 | 89 |