Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26030804 | C2 | semidirect |
| 3. #26030075 | C2 | semidirect |
| 4. #26026197 | C2 | semidirect |
| 5. #26021463 | C2 | semidirect |
| 6. #26021232 | C2 | semidirect |
| 7. #26020464 | C2 | semidirect |
| 8. #26020065 | C2 | semidirect |
| 9. C89×#1965 | C2 | semidirect |
| 134. M16×C89 | #41 | semidirect |
| 206. #1965 | D89 | semidirect |
| 209. C89 | #25690 | semidirect |
| 314. M16 | #13083573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034126 | 2 |
| #26030804 | 2 |
| #26030075 | 2 |
| #26026197 | 2 |
| #26021463 | 2 |
| #26021232 | 2 |
| #26020464 | 2 |
| #26020065 | 2 |
| C89×#1965 | 2 |
| #25690 | 89 |