Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
232 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #26018321 | C2 | semidirect |
| 4. #26018315 | C2 | semidirect |
| 75. #10623494 | M32 | semidirect |
| 97. C89 | #12017 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022055 | 2 |
| C8×#13083558 | 2 |
| #26018321 | 2 |
| #26018315 | 2 |
| C89×#2150 | 2 |
| #12017 | 89 |