Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 386 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. #26021027 | C2 | semidirect |
| 2. #26018937 | C2 | semidirect |
| 4. C2×#19151347 | C2 | semidirect |
| 6. #26018103 | C2 | semidirect |
| 178. C89 | #10551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021027 | 2 |
| #26018937 | 2 |
| #26018929 | 2 |
| C2×#19151347 | 2 |
| #26018651 | 2 |
| #26018103 | 2 |
| C89×#3141 | 2 |
| #10551 | 89 |