Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26019077 | C2 | semidirect |
| 3. #26018317 | C2 | semidirect |
| 4. #26018219 | C2 | semidirect |
| 5. #26018218 | C2 | semidirect |
| 6. #26018173 | C2 | semidirect |
| 7. C89×#1594 | C2 | semidirect |
| 47. D712 | M16 | semidirect |
| 110. #1594 | D89 | semidirect |
| 116. C89 | #12078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022126 | 2 |
| #26019077 | 2 |
| #26018317 | 2 |
| #26018219 | 2 |
| #26018218 | 2 |
| #26018173 | 2 |
| C89×#1594 | 2 |
| #12078 | 89 |