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. #26029718 | C2 | semidirect |
| 3. #26025194 | C2 | semidirect |
| 4. #26018921 | C2 | semidirect |
| 5. #26018746 | C2 | semidirect |
| 6. #26018642 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 43. #15668012 | D4 | semidirect |
| 50. #15668009 | D4 | semidirect |
| 75. C4⋊C8×C89 | D4 | semidirect |
| 76. C4⋊C8×C89 | D4 | semidirect |
| 110. C2×D356 | D8 | semidirect |
| 247. #1303 | D89 | semidirect |
| 248. C89 | #10238 | semidirect |
| 311. C4⋊C8 | D356 | semidirect |
| 312. C4⋊C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031172 | 2 |
| #26029718 | 2 |
| #26025194 | 2 |
| #26018921 | 2 |
| #26018746 | 2 |
| #26018642 | 2 |
| C89×#1303 | 2 |
| #10238 | 89 |