Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #26018304 | C2 | semidirect |
| 5. #26018234 | C2 | semidirect |
| 6. #26018222 | C2 | semidirect |
| 7. C89×#3390 | C2 | semidirect |
| 75. Q16×C89 | SD16 | semidirect |
| 140. #3390 | D89 | semidirect |
| 147. C89 | #12361 | semidirect |
| 208. Q16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022495 | 2 |
| #26022292 | 2 |
| #26019736 | 2 |
| #26018304 | 2 |
| #26018234 | 2 |
| #26018222 | 2 |
| C89×#3390 | 2 |
| #12361 | 89 |