Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 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. #26031172 | C2 | semidirect |
| 2. #26029716 | C2 | semidirect |
| 3. #26025198 | C2 | semidirect |
| 4. #26018919 | C2 | semidirect |
| 5. #26018748 | C2 | semidirect |
| 6. #26018154 | C2 | semidirect |
| 7. C89×#1478 | C2 | semidirect |
| 42. #15668012 | D4 | semidirect |
| 47. #15668009 | D4 | semidirect |
| 60. C4⋊#10623494 | D4 | semidirect |
| 75. C4⋊C8×C89 | D4 | semidirect |
| 127. C2×D4×C89 | D8 | semidirect |
| 246. #1478 | D89 | semidirect |
| 248. C89 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D89 | semidirect |
| 352. C2×D4 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031172 | 2 |
| #26029716 | 2 |
| #26025198 | 2 |
| #26018919 | 2 |
| #26018748 | 2 |
| #26018154 | 2 |
| C89×#1478 | 2 |
| #10238 | 89 |