Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 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 |
|---|---|---|
| 2. #26023160 | C2 | semidirect |
| 3. #26018747 | C2 | semidirect |
| 4. #26018644 | C2 | semidirect |
| 5. #26018154 | C2 | semidirect |
| 6. #26018110 | C2 | semidirect |
| 7. C89×#1517 | C2 | semidirect |
| 12. #19151800 | C4 | semidirect |
| 13. #19151790 | C4 | semidirect |
| 51. C4⋊#10623494 | C2×C4 | semidirect |
| 60. C4⋊Q8×C89 | C2×C4 | semidirect |
| 61. #127×C89 | C2×C4 | semidirect |
| 217. #1517 | D89 | semidirect |
| 222. C89 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D89 | semidirect |
| 254. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029712 | 2 |
| #26023160 | 2 |
| #26018747 | 2 |
| #26018644 | 2 |
| #26018154 | 2 |
| #26018110 | 2 |
| C89×#1517 | 2 |
| #9179 | 89 |