Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
458 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 458 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. #26019243 | C2 | semidirect |
| 4. #26018251 | C2 | semidirect |
| 6. #26018200 | C2 | semidirect |
| 7. C89×#2062 | C2 | semidirect |
| 113. C22⋊C4×C89 | SD16 | semidirect |
| 204. #2062 | D89 | semidirect |
| 210. C89 | #12245 | semidirect |
| 315. C22⋊C4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027020 | 2 |
| #26019243 | 2 |
| #26019175 | 2 |
| #26018251 | 2 |
| #26018248 | 2 |
| #26018200 | 2 |
| C89×#2062 | 2 |
| #12245 | 89 |