Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#15667951 | C2 | semidirect |
| 3. #26018999 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. #26018213 | C2 | semidirect |
| 6. #26018212 | C2 | semidirect |
| 7. C89×#1331 | C2 | semidirect |
| 21. C4×#13083549 | C22 | semidirect |
| 22. #19151351 | C22 | semidirect |
| 25. C4×C16×C89 | C22 | semidirect |
| 26. #335×C89 | C22 | semidirect |
| 32. D8×D89 | C8 | semidirect |
| 178. #1331 | D89 | semidirect |
| 179. C89 | #11593 | semidirect |
| 195. C4×C16 | C2×D89 | semidirect |
| 197. #335 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D89 | 2 |
| C4×#15667951 | 2 |
| #26018999 | 2 |
| #26018214 | 2 |
| #26018213 | 2 |
| #26018212 | 2 |
| C89×#1331 | 2 |
| #11593 | 89 |