Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #26022481 | C2 | semidirect |
| 4. #26018302 | C2 | semidirect |
| 5. #26018216 | C2 | semidirect |
| 7. C89×#2225 | C2 | semidirect |
| 80. Q16×C89 | SD16 | semidirect |
| 137. #2225 | D89 | semidirect |
| 142. C89 | #12370 | semidirect |
| 203. Q16 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D356 | 2 |
| #26022481 | 2 |
| #26019638 | 2 |
| #26018302 | 2 |
| #26018216 | 2 |
| #26018206 | 2 |
| C89×#2225 | 2 |
| #12370 | 89 |