Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
930 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 4. #26019296 | C2 | semidirect |
| 5. #26019262 | C2 | semidirect |
| 197. C89 | #18148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| #26030201 | 2 |
| #26024539 | 2 |
| #26019296 | 2 |
| #26019262 | 2 |
| #26018786 | 2 |
| C89×#1463 | 2 |
| #18148 | 89 |