Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. C2×#19151415 | C2 | semidirect |
| 4. C2×#19151413 | C2 | semidirect |
| 6. #26018363 | C2 | semidirect |
| 7. C89×#1385 | C2 | semidirect |
| 170. #1385 | D89 | semidirect |
| 171. C89 | #13006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151874 | 2 |
| #26028860 | 2 |
| C2×#19151415 | 2 |
| C2×#19151413 | 2 |
| #26021881 | 2 |
| #26018363 | 2 |
| C89×#1385 | 2 |
| #13006 | 89 |