Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26031170 | C2 | semidirect |
| 3. #26021180 | C2 | semidirect |
| 4. #26021171 | C2 | semidirect |
| 5. #26018747 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 7. C89×#3151 | C2 | semidirect |
| 126. M16×C89 | D8 | semidirect |
| 223. #3151 | 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 |
| #26031170 | 2 |
| #26021180 | 2 |
| #26021171 | 2 |
| #26018747 | 2 |
| #26018103 | 2 |
| C89×#3151 | 2 |
| #10192 | 89 |