Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26024522 | C2 | semidirect |
| 3. #26020351 | C2 | semidirect |
| 4. #26018781 | C2 | semidirect |
| 5. #26018578 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 7. C89×#3094 | C2 | semidirect |
| 59. #15667919 | D4 | semidirect |
| 73. C2×C4⋊C4×C89 | D4 | semidirect |
| 74. C2×C4⋊C4×C89 | D4 | semidirect |
| 83. C22⋊C8×C89 | D4 | semidirect |
| 250. #3094 | D89 | semidirect |
| 257. C89 | #9940 | semidirect |
| 304. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 305. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 329. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025184 | 2 |
| #26024522 | 2 |
| #26020351 | 2 |
| #26018781 | 2 |
| #26018578 | 2 |
| #26018106 | 2 |
| C89×#3094 | 2 |
| #9940 | 89 |