Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 238 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. C16×Dic178 | C2 | semidirect |
| 4. #26018316 | C2 | semidirect |
| 5. #26018232 | C2 | semidirect |
| 7. C8×C16×C89 | C2 | semidirect |
| 47. #13083563 | C16 | direct (N × H) |
| 67. C16×C89 | SD16 | semidirect |
| 80. Dic178 | C2×C16 | semidirect |
| 84. C8×C89 | C2×C16 | semidirect |
| 112. C8×C16 | D89 | semidirect |
| 113. C89 | C16×SD16 | semidirect |
| 173. C16 | #13083563 | direct (N × H) |
| 192. C8 | C16×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×Dic178 | 2 |
| C16×D356 | 2 |
| C8×#13083563 | 2 |
| #26018316 | 2 |
| #26018232 | 2 |
| #26018208 | 2 |
| C8×C16×C89 | 2 |
| C16×SD16 | 89 |