Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
332 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 99. C42×C89 | Q16 | semidirect |
| 165. C89 | #12259 | semidirect |
| 257. C42 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028521 | 2 |
| #26019294 | 2 |
| #26019226 | 2 |
| #26018281 | 2 |
| #26018278 | 2 |
| #26018198 | 2 |
| C89×#2060 | 2 |
| #12259 | 89 |