Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 267 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 267 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. #26022534 | C2 | direct (N × H) |
| 25. C2×C16×C89 | Q8 | semidirect |
| 44. C16×C89 | C2×Q8 | semidirect |
| 67. C2×C89 | #2254 | semidirect |
| 74. C89 | C2×#2254 | semidirect |
| 92. C2×C16 | Dic178 | semidirect |
| 114. C16 | C2×Dic178 | semidirect |
| 136. C2 | #26022534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152003 | 2 |
| #26022534 | 2 |
| C2×#19151426 | 2 |
| C2×C4×C16×C89 | 2 |
| C2×#2254 | 89 |