Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
490 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 3. #26021225 | C2 | semidirect |
| 4. #26018936 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1275 | C2 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 12. #19151949 | C4 | semidirect |
| 107. C2×C8×C89 | SD16 | semidirect |
| 181. #1275 | D89 | semidirect |
| 182. C89 | #9289 | semidirect |
| 272. C2×C8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031179 | 2 |
| #26028971 | 2 |
| #26021225 | 2 |
| #26018936 | 2 |
| #26018813 | 2 |
| #26018111 | 2 |
| C89×#1275 | 2 |
| #9289 | 89 |