Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
750 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 199 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. #26019862 | C2 | semidirect |
| 4. #26019861 | C2 | semidirect |
| 5. #26019860 | C2 | semidirect |
| 7. C89×#1710 | C2 | semidirect |
| 100. D89 | #1710 | direct (N × H) |
| 106. #1710 | D89 | direct (N × H) |
| 108. C89 | C2×#1710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D89 | 2 |
| #487×D89 | 2 |
| #26019862 | 2 |
| #26019861 | 2 |
| #26019860 | 2 |
| C82×D89 | 2 |
| C89×#1710 | 2 |
| C2×#1710 | 89 |