Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
802 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 235 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×#19151949 | C2 | semidirect |
| 3. #26019864 | C2 | direct (N × H) |
| 4. C2×C82×C89 | C2 | semidirect |
| 8. #19151949 | C22 | semidirect |
| 14. C82×C89 | C22 | semidirect |
| 69. C2×C89 | #1711 | semidirect |
| 75. C2×C82 | D89 | semidirect |
| 76. C89 | C2×#1711 | semidirect |
| 86. C82 | C2×D89 | semidirect |
| 141. C2 | #26019864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151949 | 2 |
| C2×#19151945 | 2 |
| #26019864 | 2 |
| C2×C82×C89 | 2 |
| C2×#1711 | 89 |