Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
808 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15667930 | C2 | semidirect |
| 3. #26018851 | C2 | semidirect |
| 4. #26018849 | C2 | semidirect |
| 5. #26018695 | C2 | semidirect |
| 6. #26018595 | C2 | semidirect |
| 7. C89×#1490 | C2 | semidirect |
| 260. #1490 | D89 | semidirect |
| 262. C89 | #8370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152331 | 2 |
| C4×#15667930 | 2 |
| #26018851 | 2 |
| #26018849 | 2 |
| #26018695 | 2 |
| #26018595 | 2 |
| C89×#1490 | 2 |
| #8370 | 89 |