Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 2. #26029724 | C2 | semidirect |
| 3. #26025251 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018748 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#1479 | C2 | semidirect |
| 123. C2×Q8×C89 | D8 | semidirect |
| 232. #1479 | D89 | semidirect |
| 234. C89 | #10242 | semidirect |
| 317. C2×Q8 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031172 | 2 |
| #26029724 | 2 |
| #26025251 | 2 |
| #26018919 | 2 |
| #26018748 | 2 |
| #26018154 | 2 |
| C89×#1479 | 2 |
| #10242 | 89 |