Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26018078 | C2 | semidirect |
| 5. #26018076 | C2 | semidirect |
| 6. #26018074 | C2 | semidirect |
| 7. C89×#1272 | C2 | semidirect |
| 91. C4⋊Dic89 | M16 | semidirect |
| 105. C2×Q8×C89 | M16 | semidirect |
| 212. #1272 | D89 | semidirect |
| 215. C89 | #7634 | semidirect |
| 275. C2×Q8 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022790 | 2 |
| #26020013 | 2 |
| #26019944 | 2 |
| #26018078 | 2 |
| #26018076 | 2 |
| #26018074 | 2 |
| C89×#1272 | 2 |
| #7634 | 89 |