Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
878 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 283 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. #26019868 | C2 | direct (N × H) |
| 47. C2×#10623494 | Q16 | semidirect |
| 81. #10623494 | C2×Q16 | semidirect |
| 92. C2×C89 | #1713 | semidirect |
| 100. C89 | C2×#1713 | semidirect |
| 186. C2 | #26019868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152001 | 2 |
| C2×#19151978 | 2 |
| #26019868 | 2 |
| C2×C8×#10623494 | 2 |
| C2×#494×C89 | 2 |
| C2×#1713 | 89 |