Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
678 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26031559 | C2 | semidirect |
| 2. #26031167 | C2 | semidirect |
| 3. #26030704 | C2 | semidirect |
| 4. #26021179 | C2 | semidirect |
| 5. #26018746 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#1980 | C2 | semidirect |
| 123. M16×C89 | D8 | semidirect |
| 225. #1980 | D89 | semidirect |
| 228. C89 | #10192 | semidirect |
| 337. M16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031559 | 2 |
| #26031167 | 2 |
| #26030704 | 2 |
| #26021179 | 2 |
| #26018746 | 2 |
| #26018103 | 2 |
| C89×#1980 | 2 |
| #10192 | 89 |