Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19152036 | C2 | semidirect |
| 2. #26029972 | C2 | semidirect |
| 3. #26029900 | C2 | semidirect |
| 4. C2×#19151412 | C2 | semidirect |
| 5. #26021989 | C2 | semidirect |
| 6. #26018367 | C2 | semidirect |
| 7. C89×#2117 | C2 | semidirect |
| 42. C2×Dic356 | D4 | semidirect |
| 50. C2×D712 | D4 | semidirect |
| 60. #15667948 | D4 | semidirect |
| 78. M32×C89 | D4 | semidirect |
| 217. #2117 | D89 | semidirect |
| 219. C89 | #13310 | semidirect |
| 283. M32 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| #26029972 | 2 |
| #26029900 | 2 |
| C2×#19151412 | 2 |
| #26021989 | 2 |
| #26018367 | 2 |
| C89×#2117 | 2 |
| #13310 | 89 |