Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #26033386 | C2 | semidirect |
| 2. #26030695 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26021980 | C2 | semidirect |
| 5. #26021146 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 7. C89×#3414 | C2 | semidirect |
| 64. C2×#13083549 | D4 | semidirect |
| 82. C2×Q16×C89 | D4 | semidirect |
| 86. C2×D8×C89 | D4 | semidirect |
| 94. C2×C16×C89 | D4 | semidirect |
| 236. #3414 | D89 | semidirect |
| 242. C89 | #13340 | semidirect |
| 290. C2×Q16 | C22⋊D89 | semidirect |
| 299. C2×D8 | C22⋊D89 | semidirect |
| 323. C2×C16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26030695 | 2 |
| #26021981 | 2 |
| #26021980 | 2 |
| #26021146 | 2 |
| #26018331 | 2 |
| C89×#3414 | 2 |
| #13340 | 89 |