Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
740 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26031195 | C2 | semidirect |
| 2. #26030049 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018752 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#1478 | C2 | semidirect |
| 37. #15668012 | D4 | semidirect |
| 38. #15668012 | D4 | semidirect |
| 58. C4⋊#10623494 | D4 | semidirect |
| 73. C4⋊C8×C89 | D4 | semidirect |
| 119. C2×D4×C89 | SD16 | semidirect |
| 227. #1478 | D89 | semidirect |
| 229. C89 | #10246 | semidirect |
| 291. C4⋊C8 | C22⋊D89 | semidirect |
| 324. C2×D4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031195 | 2 |
| #26030049 | 2 |
| #26025198 | 2 |
| #26018919 | 2 |
| #26018752 | 2 |
| #26018154 | 2 |
| C89×#1478 | 2 |
| #10246 | 89 |