Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26025251 | C2 | semidirect |
| 3. #26018921 | C2 | semidirect |
| 4. #26018747 | C2 | semidirect |
| 5. #26018647 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#3037 | C2 | semidirect |
| 111. C2×Q8×C89 | D8 | semidirect |
| 228. #3037 | D89 | semidirect |
| 234. C89 | #10242 | semidirect |
| 317. C2×Q8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26025251 | 2 |
| #26018921 | 2 |
| #26018747 | 2 |
| #26018647 | 2 |
| #26018153 | 2 |
| C89×#3037 | 2 |
| #10242 | 89 |