Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #26018223 | C2 | semidirect |
| 5. #26018222 | C2 | semidirect |
| 6. #26018221 | C2 | semidirect |
| 7. C89×#1334 | C2 | semidirect |
| 31. Q16×D89 | C8 | semidirect |
| 159. #1334 | D89 | semidirect |
| 160. C89 | #11600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q16×D89 | 2 |
| #26021845 | 2 |
| #26018997 | 2 |
| #26018223 | 2 |
| #26018222 | 2 |
| #26018221 | 2 |
| C89×#1334 | 2 |
| #11600 | 89 |