Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #26021214 | C2 | semidirect |
| 3. #26020409 | C2 | semidirect |
| 4. C2×C8×#10623494 | C2 | semidirect |
| 16. #492×C89 | C4 | semidirect |
| 46. C2×#10623494 | SD16 | semidirect |
| 101. C8×C89 | #102 | semidirect |
| 131. C89 | #9820 | semidirect |
| 136. #492 | Dic89 | semidirect |
| 228. C8 | #15667933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021214 | 2 |
| #26021059 | 2 |
| #26020409 | 2 |
| C2×C8×#10623494 | 2 |
| C2×#492×C89 | 2 |
| #9820 | 89 |