Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
662 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×#15667955 | C2 | semidirect |
| 3. C2×#19151398 | C2 | semidirect |
| 4. #26018330 | C2 | semidirect |
| 5. C89×#1969 | C2 | semidirect |
| 36. C2×#13083549 | D4 | semidirect |
| 41. C2×Q16×C89 | D4 | semidirect |
| 106. C2×C4×C89 | SD32 | semidirect |
| 148. #1969 | D89 | semidirect |
| 150. C89 | #13328 | semidirect |
| 171. C2×Q16 | D356 | semidirect |
| 256. C2×C4 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| C2×#19151975 | 2 |
| C2×#19151398 | 2 |
| #26018330 | 2 |
| C89×#1969 | 2 |
| #13328 | 89 |