Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
844 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018371 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 6. C23×C4×D89 | C4 | semidirect |
| 12. #19151470 | C4 | semidirect |
| 14. #19151453 | C4 | semidirect |
| 17. C4×C22⋊Dic89 | C4 | semidirect |
| 18. #19151386 | C4 | direct (N × H) |
| 46. #15667927 | C2×C4 | semidirect |
| 62. #100×C89 | C2×C4 | semidirect |
| 71. C23×D89 | C42 | semidirect |
| 98. C22⋊Dic89 | C42 | semidirect |
| 227. C4×C89 | AΣL(1,𝔽16) | semidirect |
| 244. C4×#100 | D89 | semidirect |
| 247. C89 | C4×AΣL(1,𝔽16) | semidirect |
| 298. #100 | C4×D89 | semidirect |
| 473. C4 | #19151386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667980 | 2 |
| C2×#19151386 | 2 |
| C4×#15667927 | 2 |
| #26018371 | 2 |
| C4×#100×C89 | 2 |
| C4×AΣL(1,𝔽16) | 89 |