Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 2. C2×C4⋊#13083549 | C2 | semidirect |
| 3. #26018305 | C2 | semidirect |
| 4. #26018294 | C2 | semidirect |
| 5. C89×#1568 | C2 | semidirect |
| 143. #1568 | D89 | semidirect |
| 146. C89 | #11978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030822 | 2 |
| C2×C4⋊#13083549 | 2 |
| #26018305 | 2 |
| #26018294 | 2 |
| C89×#1568 | 2 |
| #11978 | 89 |