Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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×C32×D89 | C2 | semidirect |
| 3. C4⋊#15667918 | C2 | semidirect |
| 4. #26018389 | C2 | semidirect |
| 5. C4×C32×C89 | C2 | semidirect |
| 27. C32×C89 | D4 | semidirect |
| 47. D356 | C32 | direct (N × H) |
| 57. C2×D89 | C2×C32 | semidirect |
| 59. C4×C89 | C2×C32 | semidirect |
| 72. C4×C32 | D89 | semidirect |
| 73. C89 | D4×C32 | semidirect |
| 95. C32 | D356 | direct (N × H) |
| 128. C4 | C32×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D89 | 2 |
| C16×D356 | 2 |
| C4⋊#15667918 | 2 |
| #26018389 | 2 |
| C4×C32×C89 | 2 |
| D4×C32 | 89 |