Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #26018317 | C2 | semidirect |
| 4. #26018222 | C2 | semidirect |
| 6. #26018173 | C2 | semidirect |
| 7. C89×#1579 | C2 | semidirect |
| 26. #15667955 | C8 | semidirect |
| 54. #13083549 | C2×C8 | semidirect |
| 57. Q16×C89 | C2×C8 | semidirect |
| 105. #1579 | D89 | semidirect |
| 110. C89 | #12065 | semidirect |
| 151. Q16 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022114 | 2 |
| #26019077 | 2 |
| #26018317 | 2 |
| #26018222 | 2 |
| #26018218 | 2 |
| #26018173 | 2 |
| C89×#1579 | 2 |
| #12065 | 89 |