Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 476 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. #26029135 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021151 | C2 | semidirect |
| 5. #26018359 | C2 | semidirect |
| 6. #26018337 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 10. #19152039 | C4 | semidirect |
| 12. #19152034 | C4 | semidirect |
| 50. #15667952 | C2×C4 | semidirect |
| 65. C2×Q16×C89 | C2×C4 | semidirect |
| 67. C2×D8×C89 | C2×C4 | semidirect |
| 193. C2×#360 | D89 | semidirect |
| 197. C89 | #13030 | semidirect |
| 230. C2×Q16 | C4×D89 | semidirect |
| 234. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26029135 | 2 |
| #26021989 | 2 |
| #26021151 | 2 |
| #26018359 | 2 |
| #26018337 | 2 |
| C2×#360×C89 | 2 |
| #13030 | 89 |