Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021238 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018104 | C2 | semidirect |
| 7. C89×#1511 | C2 | semidirect |
| 10. #19151911 | C4 | semidirect |
| 13. #19151737 | C4 | semidirect |
| 56. C22⋊#10623494 | C2×C4 | semidirect |
| 61. C22×Q8×C89 | C2×C4 | semidirect |
| 69. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 233. #1511 | D89 | semidirect |
| 237. C89 | #9341 | semidirect |
| 261. C22×Q8 | C4×D89 | semidirect |
| 281. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26023411 | 2 |
| #26021238 | 2 |
| #26018769 | 2 |
| #26018157 | 2 |
| #26018104 | 2 |
| C89×#1511 | 2 |
| #9341 | 89 |