Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
404 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 49. C22×Q8×C89 | Q8 | semidirect |
| 57. C2×C4⋊C4×C89 | Q8 | semidirect |
| 198. C89 | #10383 | semidirect |
| 219. C22×Q8 | Dic178 | semidirect |
| 232. C2×C4⋊C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026424 | 2 |
| #26021238 | 2 |
| #26018772 | 2 |
| #26018159 | 2 |
| #26018137 | 2 |
| #26018104 | 2 |
| C89×#1511 | 2 |
| #10383 | 89 |