Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26025206 | C2 | semidirect |
| 3. #26018933 | C2 | semidirect |
| 4. #26018747 | C2 | semidirect |
| 5. #26018642 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#3206 | C2 | semidirect |
| 84. C2×D356 | SD16 | semidirect |
| 217. #3206 | D89 | semidirect |
| 224. C89 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029712 | 2 |
| #26025206 | 2 |
| #26018933 | 2 |
| #26018747 | 2 |
| #26018642 | 2 |
| #26018154 | 2 |
| C89×#3206 | 2 |
| #10240 | 89 |