Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
194 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 194 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 |
|---|---|---|
| 2. #26018447 | C2 | semidirect |
| 4. #26018386 | C2 | semidirect |
| 5. C89×#1397 | C2 | semidirect |
| 84. #1397 | D89 | semidirect |
| 85. C89 | #13640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D89 | 2 |
| #26018447 | 2 |
| #26018389 | 2 |
| #26018386 | 2 |
| C89×#1397 | 2 |
| #13640 | 89 |