Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26019138 | C2 | semidirect |
| 3. #26018323 | C2 | semidirect |
| 4. #26018213 | C2 | semidirect |
| 5. #26018212 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C89×#1589 | C2 | semidirect |
| 54. #13083549 | M16 | semidirect |
| 88. C8×C89 | D16 | semidirect |
| 114. #1589 | D89 | semidirect |
| 119. C89 | #12081 | semidirect |
| 201. C8 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667953 | 2 |
| #26019138 | 2 |
| #26018323 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| C8×#13083549 | 2 |
| C89×#1589 | 2 |
| #12081 | 89 |