Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 548 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. #26018816 | C2 | semidirect |
| 4. #26018681 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#3104 | C2 | semidirect |
| 88. C2×D356 | Q16 | semidirect |
| 214. #3104 | D89 | semidirect |
| 221. C89 | #10002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030045 | 2 |
| #26025610 | 2 |
| #26018816 | 2 |
| #26018681 | 2 |
| #26018644 | 2 |
| #26018111 | 2 |
| C89×#3104 | 2 |
| #10002 | 89 |