Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
550 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031380 | C2 | semidirect |
| 3. #26018933 | C2 | semidirect |
| 4. #26018650 | C2 | semidirect |
| 5. #26018573 | C2 | semidirect |
| 6. #26018149 | C2 | semidirect |
| 7. C2×#474×C89 | C2 | semidirect |
| 210. C2×#474 | D89 | semidirect |
| 216. C89 | #10188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031380 | 2 |
| #26029716 | 2 |
| #26018933 | 2 |
| #26018650 | 2 |
| #26018573 | 2 |
| #26018149 | 2 |
| C2×#474×C89 | 2 |
| #10188 | 89 |