Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #26028843 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. C2×#19151407 | C2 | semidirect |
| 5. #26021881 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 13. #19151874 | C4 | semidirect |
| 14. #19151869 | C4 | semidirect |
| 40. C2×Dic356 | C2×C4 | semidirect |
| 42. C2×D712 | C2×C4 | semidirect |
| 73. #108×C89 | C2×C4 | semidirect |
| 200. #1383 | D89 | semidirect |
| 201. C89 | #13005 | semidirect |
| 260. #108 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029973 | 2 |
| #26028843 | 2 |
| #26021989 | 2 |
| C2×#19151407 | 2 |
| #26021881 | 2 |
| #26018366 | 2 |
| C89×#1383 | 2 |
| #13005 | 89 |