Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C2×#19152039 | C2 | semidirect |
| 3. C2×#19151407 | C2 | semidirect |
| 4. #26021972 | C2 | semidirect |
| 5. C2×#19151380 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C2×#470×C89 | C2 | semidirect |
| 50. #15667952 | D4 | semidirect |
| 64. C2×Q16×C89 | D4 | semidirect |
| 79. #106×C89 | D4 | semidirect |
| 214. C2×#470 | D89 | semidirect |
| 219. C89 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D89 | semidirect |
| 289. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26029861 | 2 |
| C2×#19151407 | 2 |
| #26021972 | 2 |
| C2×#19151380 | 2 |
| #26018359 | 2 |
| C2×#470×C89 | 2 |
| #13317 | 89 |