Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 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 |
|---|---|---|
| 3. #26021225 | C2 | semidirect |
| 4. #26021224 | C2 | semidirect |
| 6. #26018134 | C2 | semidirect |
| 7. C89×#1295 | C2 | semidirect |
| 13. #19151992 | C4 | semidirect |
| 44. #15668012 | C2×C4 | semidirect |
| 74. #97×C89 | C2×C4 | semidirect |
| 227. #1295 | D89 | semidirect |
| 228. C89 | #9003 | semidirect |
| 291. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151992 | 2 |
| #26023423 | 2 |
| #26021225 | 2 |
| #26021224 | 2 |
| C2×#19151337 | 2 |
| #26018134 | 2 |
| C89×#1295 | 2 |
| #9003 | 89 |