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. C2×#19152033 | C2 | semidirect |
| 2. #26029900 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. #26021988 | C2 | semidirect |
| 5. #26021880 | C2 | semidirect |
| 6. #26018366 | C2 | semidirect |
| 7. C89×#3067 | C2 | semidirect |
| 48. #15667952 | D4 | semidirect |
| 65. C2×Q16×C89 | D4 | semidirect |
| 67. C2×D8×C89 | D4 | semidirect |
| 78. #108×C89 | D4 | semidirect |
| 213. #3067 | D89 | semidirect |
| 219. C89 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D89 | semidirect |
| 263. C2×D8 | C22⋊D89 | semidirect |
| 287. #108 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| #26029900 | 2 |
| C2×#19151410 | 2 |
| #26021988 | 2 |
| #26021880 | 2 |
| #26018366 | 2 |
| C89×#3067 | 2 |
| #13310 | 89 |