Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
340 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 4. #26018428 | C2 | semidirect |
| 5. #26018427 | C2 | semidirect |
| 6. #26018426 | C2 | semidirect |
| 7. C89×#1414 | C2 | semidirect |
| 8. #125×D89 | C4 | semidirect |
| 10. #19151955 | C4 | semidirect |
| 12. #19151953 | C4 | semidirect |
| 19. C4×C8×D89 | C4 | semidirect |
| 31. #15668004 | C2×C4 | semidirect |
| 53. C4×#10623494 | C2×C4 | semidirect |
| 55. #125×C89 | C2×C4 | semidirect |
| 61. C4×C8×C89 | C2×C4 | semidirect |
| 162. D89 | #1414 | direct (N × H) |
| 169. #1414 | D89 | direct (N × H) |
| 170. C89 | C2×#1414 | semidirect |
| 197. #125 | C4×D89 | semidirect |
| 224. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #488×D89 | 2 |
| #355×D89 | 2 |
| #354×D89 | 2 |
| #26018428 | 2 |
| #26018427 | 2 |
| #26018426 | 2 |
| C89×#1414 | 2 |
| C2×#1414 | 89 |