Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19151395 | C2 | semidirect |
| 3. C2×#19151394 | C2 | semidirect |
| 4. C2×#19151394 | C2 | semidirect |
| 5. #26020246 | C2 | semidirect |
| 6. #101×Dic89 | C2 | semidirect |
| 7. C2×#355×C89 | C2 | semidirect |
| 63. #15667931 | D4 | semidirect |
| 81. #101×C89 | D4 | semidirect |
| 240. Dic89 | #355 | semidirect |
| 253. C2×#355 | D89 | semidirect |
| 256. C89 | #13226 | semidirect |
| 327. #101 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025252 | 2 |
| C2×#19151395 | 2 |
| C2×#19151394 | 2 |
| #26020246 | 2 |
| #101×Dic89 | 2 |
| C2×#355×C89 | 2 |
| #13226 | 89 |