Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #26018446 | C2 | semidirect |
| 5. #26018445 | C2 | semidirect |
| 6. #26018444 | C2 | semidirect |
| 7. C89×#1420 | C2 | semidirect |
| 118. D89 | #1420 | direct (N × H) |
| 125. #1420 | D89 | direct (N × H) |
| 126. C89 | C2×#1420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D89 | 2 |
| M64×D89 | 2 |
| #368×D89 | 2 |
| #26018446 | 2 |
| #26018445 | 2 |
| #26018444 | 2 |
| C89×#1420 | 2 |
| C2×#1420 | 89 |