Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1278 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1278 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151749 | C2 | semidirect |
| 2. #26026060 | C2 | semidirect |
| 4. C2×#19151336 | C2 | semidirect |
| 5. C2×#19151321 | C2 | semidirect |
| 6. #26018130 | C2 | semidirect |
| 7. C89×#1786 | C2 | semidirect |
| 32. C22×Dic178 | D4 | semidirect |
| 48. C2×C4⋊Dic89 | D4 | semidirect |
| 63. C22⋊#10623494 | D4 | semidirect |
| 77. C2×C4⋊C4×C89 | D4 | semidirect |
| 91. C23×D89 | SD16 | semidirect |
| 312. #1786 | D89 | semidirect |
| 316. C89 | #9922 | semidirect |
| 369. C2×C4⋊C4 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151749 | 2 |
| #26026060 | 2 |
| C2×#19151506 | 2 |
| C2×#19151336 | 2 |
| C2×#19151321 | 2 |
| #26018130 | 2 |
| C89×#1786 | 2 |
| #9922 | 89 |