Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26019136 | C2 | semidirect |
| 3. #26019046 | C2 | semidirect |
| 4. #26018212 | C2 | semidirect |
| 5. #26018212 | C2 | semidirect |
| 6. #26018171 | C2 | semidirect |
| 7. C89×#1371 | C2 | semidirect |
| 51. D712 | M16 | semidirect |
| 91. #10623494 | D16 | semidirect |
| 115. #1371 | D89 | semidirect |
| 119. C89 | #12069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1424 | 2 |
| #26019136 | 2 |
| #26019046 | 2 |
| #26018212 | 2 |
| #26018171 | 2 |
| C89×#1371 | 2 |
| #12069 | 89 |