Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
994 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 331 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 |
|---|---|---|
| 1. C2×#19151996 | C2 | semidirect |
| 3. #26019839 | C2 | direct (N × H) |
| 4. C2×C82×C89 | C2 | semidirect |
| 9. #19151996 | C22 | semidirect |
| 14. C82×C89 | C22 | semidirect |
| 42. C2×C8×C89 | SD16 | semidirect |
| 58. C8×C89 | C2×SD16 | semidirect |
| 67. C2×C89 | #1705 | semidirect |
| 73. C2×C82 | D89 | semidirect |
| 74. C89 | C2×#1705 | semidirect |
| 84. C82 | C2×D89 | semidirect |
| 110. C2×C8 | #13083563 | semidirect |
| 128. C8 | C2×#13083563 | semidirect |
| 137. C2 | #26019839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151996 | 2 |
| C2×#19151971 | 2 |
| #26019839 | 2 |
| C2×C82×C89 | 2 |
| C2×#1705 | 89 |