Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26018321 | C2 | semidirect |
| 5. #26018316 | C2 | semidirect |
| 6. #26018315 | C2 | semidirect |
| 7. C89×#1370 | C2 | semidirect |
| 114. #1370 | D89 | semidirect |
| 117. C89 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022054 | 2 |
| C4⋊C16×D89 | 2 |
| C8×#13083557 | 2 |
| #26018321 | 2 |
| #26018316 | 2 |
| #26018315 | 2 |
| C89×#1370 | 2 |
| #12016 | 89 |