Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26018803 | C2 | semidirect |
| 4. #26018673 | C2 | semidirect |
| 5. #26018118 | C2 | semidirect |
| 6. #26018113 | C2 | semidirect |
| 26. #501×C89 | C4 | semidirect |
| 27. #501×C89 | C4 | semidirect |
| 28. #489×C89 | C4 | semidirect |
| 29. #489×C89 | C4 | semidirect |
| 197. C89 | #9369 | semidirect |
| 200. #501 | Dic89 | semidirect |
| 201. #501 | Dic89 | semidirect |
| 202. #489 | Dic89 | semidirect |
| 203. #489 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029239 | 2 |
| #26018829 | 2 |
| #26018803 | 2 |
| #26018673 | 2 |
| #26018118 | 2 |
| #26018113 | 2 |
| C89×#3240 | 2 |
| #9369 | 89 |