Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022171 | C2 | semidirect |
| 3. #26021262 | C2 | semidirect |
| 4. #26018262 | C2 | semidirect |
| 5. C89×#1314 | C2 | semidirect |
| 6. C22×Dic356 | C22 | semidirect |
| 16. #19151361 | C22 | semidirect |
| 18. C22⋊C16×C89 | C22 | semidirect |
| 94. C23×C89 | SD32 | semidirect |
| 162. #1314 | D89 | semidirect |
| 163. C89 | #12105 | semidirect |
| 175. C22⋊C16 | C2×D89 | semidirect |
| 256. C23 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031003 | 2 |
| #26022171 | 2 |
| #26021262 | 2 |
| #26018262 | 2 |
| C89×#1314 | 2 |
| #12105 | 89 |