Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
250 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26018385 | C2 | semidirect |
| 4. C4×#15667918 | C2 | semidirect |
| 5. C4×C32×C89 | C2 | semidirect |
| 9. #19151431 | C4 | direct (N × H) |
| 26. #15667918 | C2×C4 | semidirect |
| 30. C32×C89 | C2×C4 | semidirect |
| 63. C4×C89 | M64 | semidirect |
| 76. C4×C32 | D89 | semidirect |
| 77. C89 | C4×M64 | semidirect |
| 102. C32 | C4×D89 | semidirect |
| 137. C4 | #19151431 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151431 | 2 |
| C4×C16×D89 | 2 |
| #26018385 | 2 |
| C4×#15667918 | 2 |
| C4×C32×C89 | 2 |
| C4×M64 | 89 |