Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
828 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19151793 | C2 | semidirect |
| 2. #26021057 | C2 | semidirect |
| 3. C2×D4⋊#10623494 | C2 | semidirect |
| 4. #26018135 | C2 | semidirect |
| 5. C89×#2537 | C2 | semidirect |
| 29. #15668009 | D4 | semidirect |
| 31. C4⋊#10623494 | D4 | semidirect |
| 77. C2×D4×C89 | D8 | semidirect |
| 178. #2537 | D89 | semidirect |
| 182. C89 | #10228 | semidirect |
| 247. C2×D4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151793 | 2 |
| #26021057 | 2 |
| C2×D4⋊#10623494 | 2 |
| #26018135 | 2 |
| C89×#2537 | 2 |
| #10228 | 89 |