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 |
|---|---|---|
| 3. #26018315 | C2 | semidirect |
| 4. Q8⋊#13083549 | C2 | semidirect |
| 6. C16×#10623494 | C2 | semidirect |
| 7. Q8×C16×C89 | C2 | semidirect |
| 46. #13083561 | C16 | direct (N × H) |
| 67. C16×C89 | SD16 | semidirect |
| 70. Q8×C89 | C2×C16 | semidirect |
| 88. #10623494 | C2×C16 | semidirect |
| 106. Q8×C16 | D89 | semidirect |
| 113. C89 | C16×SD16 | semidirect |
| 173. C16 | #13083561 | direct (N × H) |
| 176. Q8 | C16×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C16×D356 | 2 |
| C8×#13083561 | 2 |
| #26018315 | 2 |
| Q8⋊#13083549 | 2 |
| #26018206 | 2 |
| C16×#10623494 | 2 |
| Q8×C16×C89 | 2 |
| C16×SD16 | 89 |