Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 1. #26033354 | C2 | semidirect |
| 3. #26021980 | C2 | semidirect |
| 4. #26020299 | C2 | semidirect |
| 5. #26018352 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#2143 | C2 | semidirect |
| 45. C2×#13083549 | D4 | semidirect |
| 67. C2×C16×C89 | D4 | semidirect |
| 184. #2143 | D89 | semidirect |
| 188. C89 | #13076 | semidirect |
| 240. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029910 | 2 |
| #26021980 | 2 |
| #26020299 | 2 |
| #26018352 | 2 |
| #26018351 | 2 |
| C89×#2143 | 2 |
| #13076 | 89 |