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×#19152039 | C2 | semidirect |
| 3. C2×#19151853 | C2 | semidirect |
| 4. C2×#19151409 | C2 | semidirect |
| 5. C2×#19151379 | C2 | semidirect |
| 6. #26018357 | C2 | semidirect |
| 7. C89×#2141 | C2 | semidirect |
| 60. #15667952 | D4 | semidirect |
| 63. #15667944 | D4 | semidirect |
| 73. C2×Q16×C89 | D4 | semidirect |
| 216. #2141 | D89 | semidirect |
| 219. C89 | #13317 | semidirect |
| 256. C2×Q16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26029862 | 2 |
| C2×#19151853 | 2 |
| C2×#19151409 | 2 |
| C2×#19151379 | 2 |
| #26018357 | 2 |
| C89×#2141 | 2 |
| #13317 | 89 |