Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19151421 | C2 | semidirect |
| 3. C2×#19151420 | C2 | semidirect |
| 6. #26018352 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 19. #19151377 | C4 | semidirect |
| 40. C2×#13083549 | C2×C4 | semidirect |
| 52. C2×C16×C89 | C2×C4 | semidirect |
| 134. C2×D89 | #365 | semidirect |
| 154. #1383 | D89 | semidirect |
| 155. C89 | #12929 | semidirect |
| 194. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#106×D89 | 2 |
| C2×#19151421 | 2 |
| C2×#19151420 | 2 |
| #26021862 | 2 |
| #26020287 | 2 |
| #26018352 | 2 |
| C89×#1383 | 2 |
| #12929 | 89 |