Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
7118 conjugacy classes of subgroups; only the 1459 normal subgroups are shown.
This group has 7118 conjugacy classes of subgroups — too many to draw. Only its 1459 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. C2×#19151509 | C2 | direct (N × H) |
| 3. C22×#15667919 | C2 | semidirect |
| 4. C24×Q8×C89 | C2 | semidirect |
| 9. #19151509 | C22 | direct (N × H) |
| 10. C2×#15667919 | C22 | semidirect |
| 12. C23×Q8×C89 | C22 | semidirect |
| 16. C24×D89 | Q8 | semidirect |
| 23. #15667919 | C23 | semidirect |
| 27. C22×Q8×C89 | C23 | semidirect |
| 36. C23×D89 | C2×Q8 | semidirect |
| 66. C22×D89 | C22×Q8 | semidirect |
| 74. C22×C89 | #393 | semidirect |
| 88. C2×C89 | C2×#393 | semidirect |
| 93. C24×Q8 | D89 | semidirect |
| 97. C89 | C22×#393 | semidirect |
| 100. C23×Q8 | C2×D89 | semidirect |
| 114. C22×Q8 | C22×D89 | semidirect |
| 171. C22 | #19151509 | direct (N × H) |
| 181. C2 | C2×#19151509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13083551 | 2 |
| C2×#19151509 | 2 |
| C22×#15667919 | 2 |
| C24×Q8×C89 | 2 |
| C22×#393 | 89 |