Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26020288 | C2 | semidirect |
| 4. #26018128 | C2 | semidirect |
| 104. C23×C89 | #108 | semidirect |
| 123. C2×C4×C89 | #108 | semidirect |
| 169. C89 | #8612 | semidirect |
| 268. C23 | #15667947 | semidirect |
| 287. C2×C4 | #15667947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#10623494 | 2 |
| #26020288 | 2 |
| #26018590 | 2 |
| #26018128 | 2 |
| C89×#1465 | 2 |
| #8612 | 89 |