Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1350 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 459 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. C42×D356 | C2 | semidirect |
| 3. C4×#15667946 | C2 | semidirect |
| 4. C4×#15667934 | C2 | semidirect |
| 5. C42×C8×C89 | C2 | semidirect |
| 9. C4×D712 | C4 | direct (N × H) |
| 22. C4×D356 | C2×C4 | semidirect |
| 27. #15667946 | C2×C4 | semidirect |
| 28. #15667934 | C2×C4 | semidirect |
| 36. C4×C8×C89 | C2×C4 | semidirect |
| 44. D712 | C42 | direct (N × H) |
| 56. C42×C89 | D8 | semidirect |
| 74. D356 | C2×C42 | semidirect |
| 77. C8×C89 | C2×C42 | semidirect |
| 85. C4×C89 | C4×D8 | semidirect |
| 98. C42×C8 | D89 | semidirect |
| 99. C89 | C42×D8 | semidirect |
| 129. C4×C8 | C4×D89 | semidirect |
| 150. C42 | D712 | direct (N × H) |
| 171. C8 | C42×D89 | semidirect |
| 180. C4 | C4×D712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D712 | 2 |
| C42×D356 | 2 |
| C4×#15667946 | 2 |
| C4×#15667934 | 2 |
| C42×C8×C89 | 2 |
| C42×D8 | 89 |