Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028971 | C2 | semidirect |
| 3. #26021076 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018813 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1275 | C2 | semidirect |
| 11. #19151975 | C4 | semidirect |
| 12. #19151945 | C4 | semidirect |
| 114. C2×C8×C89 | D8 | semidirect |
| 202. #1275 | D89 | semidirect |
| 203. C89 | #9293 | semidirect |
| 304. C2×C8 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031172 | 2 |
| #26028971 | 2 |
| #26021076 | 2 |
| #26018919 | 2 |
| #26018813 | 2 |
| #26018111 | 2 |
| C89×#1275 | 2 |
| #9293 | 89 |