Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
726 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. #26028583 | C2 | semidirect |
| 3. #26020320 | C2 | semidirect |
| 4. #26018820 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#2854 | C2 | semidirect |
| 137. C22×C4×C89 | D8 | semidirect |
| 278. #2854 | D89 | semidirect |
| 283. C89 | #10321 | semidirect |
| 398. C22×C4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| #26028583 | 2 |
| #26020320 | 2 |
| #26018820 | 2 |
| #26018819 | 2 |
| #26018119 | 2 |
| C89×#2854 | 2 |
| #10321 | 89 |