Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26018566 | C2 | semidirect |
| 3. #26018185 | C2 | semidirect |
| 4. #26018183 | C2 | semidirect |
| 5. C89×#1458 | C2 | semidirect |
| 27. C2×#13083574 | C8 | semidirect |
| 205. #1458 | D89 | semidirect |
| 208. C89 | #11431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022740 | 2 |
| #26018566 | 2 |
| #26018185 | 2 |
| #26018183 | 2 |
| C89×#1458 | 2 |
| #11431 | 89 |