Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021179 | C2 | semidirect |
| 3. #26021092 | C2 | semidirect |
| 4. #26019004 | C2 | semidirect |
| 5. #26018929 | C2 | semidirect |
| 6. #26018155 | C2 | semidirect |
| 7. C89×#1980 | C2 | semidirect |
| 111. M16×C89 | D8 | semidirect |
| 210. #1980 | D89 | semidirect |
| 215. C89 | #10500 | semidirect |
| 314. M16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26021179 | 2 |
| #26021092 | 2 |
| #26019004 | 2 |
| #26018929 | 2 |
| #26018155 | 2 |
| C89×#1980 | 2 |
| #10500 | 89 |