Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
696 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26030261 | C2 | semidirect |
| 2. #26030260 | C2 | semidirect |
| 4. #26021232 | C2 | semidirect |
| 5. #26018676 | C2 | semidirect |
| 6. #26018080 | C2 | semidirect |
| 7. C89×#1486 | C2 | semidirect |
| 38. #15668012 | D4 | semidirect |
| 39. #15668012 | D4 | semidirect |
| 66. C4×#10623494 | D4 | semidirect |
| 83. C4×C8×C89 | D4 | semidirect |
| 118. C4×Dic89 | SD16 | semidirect |
| 230. #1486 | D89 | semidirect |
| 232. C89 | #10015 | semidirect |
| 306. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030261 | 2 |
| #26030260 | 2 |
| #26023531 | 2 |
| #26021232 | 2 |
| #26018676 | 2 |
| #26018080 | 2 |
| C89×#1486 | 2 |
| #10015 | 89 |