Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
394 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26019294 | C2 | semidirect |
| 3. #26019226 | C2 | semidirect |
| 4. #26018281 | C2 | semidirect |
| 5. #26018278 | C2 | semidirect |
| 87. C2×D4×C89 | Q16 | semidirect |
| 187. C89 | #12223 | semidirect |
| 250. C2×D4 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027953 | 2 |
| #26019294 | 2 |
| #26019226 | 2 |
| #26018281 | 2 |
| #26018278 | 2 |
| #26018184 | 2 |
| C89×#2027 | 2 |
| #12223 | 89 |