Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
446 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #26021724 | C2 | semidirect |
| 4. #26018078 | C2 | semidirect |
| 5. #26018076 | C2 | semidirect |
| 7. C89×#2072 | C2 | semidirect |
| 198. #2072 | D89 | semidirect |
| 202. C89 | #7789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027270 | 2 |
| #26021781 | 2 |
| #26021724 | 2 |
| #26018078 | 2 |
| #26018076 | 2 |
| #26018072 | 2 |
| C89×#2072 | 2 |
| #7789 | 89 |