Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
578 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26031249 | C2 | semidirect |
| 2. #26031239 | C2 | semidirect |
| 3. #26030716 | C2 | semidirect |
| 4. #26018722 | C2 | semidirect |
| 5. #26018668 | C2 | semidirect |
| 6. #26018125 | C2 | semidirect |
| 7. C89×#1469 | C2 | semidirect |
| 218. #1469 | D89 | semidirect |
| 220. C89 | #10120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031249 | 2 |
| #26031239 | 2 |
| #26030716 | 2 |
| #26018722 | 2 |
| #26018668 | 2 |
| #26018125 | 2 |
| C89×#1469 | 2 |
| #10120 | 89 |