Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26031255 | C2 | semidirect |
| 2. #26030352 | C2 | semidirect |
| 4. #26021196 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1527 | C2 | semidirect |
| 39. #15668012 | D4 | semidirect |
| 40. #15668012 | D4 | semidirect |
| 61. C4⋊#10623494 | D4 | semidirect |
| 82. #97×C89 | D4 | semidirect |
| 232. #1527 | D89 | semidirect |
| 235. C89 | #10008 | semidirect |
| 309. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031255 | 2 |
| #26030352 | 2 |
| #26025192 | 2 |
| #26021196 | 2 |
| #26018696 | 2 |
| #26018107 | 2 |
| C89×#1527 | 2 |
| #10008 | 89 |