Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
752 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 752 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. #26021907 | C2 | semidirect |
| 3. #26021903 | C2 | semidirect |
| 4. #26020802 | C2 | semidirect |
| 5. #26020797 | C2 | semidirect |
| 6. #26020636 | C2 | semidirect |
| 7. C89×#2132 | C2 | semidirect |
| 10. #19152335 | C4 | semidirect |
| 14. #19152278 | C4 | semidirect |
| 285. #2132 | D89 | semidirect |
| 291. C89 | #12770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034679 | 2 |
| #26021907 | 2 |
| #26021903 | 2 |
| #26020802 | 2 |
| #26020797 | 2 |
| #26020636 | 2 |
| C89×#2132 | 2 |
| #12770 | 89 |