Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
692 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 692 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. #26031239 | C2 | semidirect |
| 2. #26030344 | C2 | semidirect |
| 3. #26025192 | C2 | semidirect |
| 4. #26021171 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. #26018107 | C2 | semidirect |
| 7. C89×#1527 | C2 | semidirect |
| 40. #15668012 | D4 | semidirect |
| 41. #15668009 | D4 | semidirect |
| 61. C4⋊#10623494 | D4 | semidirect |
| 83. #97×C89 | D4 | semidirect |
| 243. #1527 | D89 | semidirect |
| 246. C89 | #10004 | semidirect |
| 321. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26030344 | 2 |
| #26025192 | 2 |
| #26021171 | 2 |
| #26018696 | 2 |
| #26018107 | 2 |
| C89×#1527 | 2 |
| #10004 | 89 |