Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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. #26019870 | C2 | semidirect |
| 4. #26019869 | C2 | semidirect |
| 5. #26019868 | C2 | semidirect |
| 7. C89×#1713 | C2 | semidirect |
| 57. C8×D89 | Q16 | semidirect |
| 82. C8×C89 | C2×Q16 | semidirect |
| 84. #10623494 | C2×Q16 | semidirect |
| 97. D89 | #1713 | direct (N × H) |
| 103. #1713 | D89 | direct (N × H) |
| 105. C89 | C2×#1713 | semidirect |
| 182. C8 | Q16×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D89 | 2 |
| #494×D89 | 2 |
| #26019870 | 2 |
| #26019869 | 2 |
| #26019868 | 2 |
| C82×D89 | 2 |
| C89×#1713 | 2 |
| C2×#1713 | 89 |