Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
346 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 83. C2×Q8×C89 | Q16 | semidirect |
| 168. C89 | #12222 | semidirect |
| 230. C2×Q8 | #13083564 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021413 | 2 |
| #26019293 | 2 |
| #26019225 | 2 |
| #26018282 | 2 |
| #26018279 | 2 |
| #26018186 | 2 |
| C89×#2799 | 2 |
| #12222 | 89 |