Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19151957 | C2 | semidirect |
| 2. #26021071 | C2 | semidirect |
| 3. C2×#19151338 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 25. #15668012 | D4 | semidirect |
| 32. #15667923 | D4 | semidirect |
| 137. C89 | #10085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151957 | 2 |
| #26021071 | 2 |
| C2×#19151338 | 2 |
| #26018133 | 2 |
| C89×#2819 | 2 |
| #10085 | 89 |