Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
234 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #26019138 | C2 | semidirect |
| 3. #26018326 | C2 | semidirect |
| 4. #26018214 | C2 | semidirect |
| 5. C89×#1311 | C2 | semidirect |
| 45. C16×C89 | M16 | semidirect |
| 79. #1311 | D89 | semidirect |
| 80. C89 | #12086 | semidirect |
| 120. C16 | #13083557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D1424 | 2 |
| #26019138 | 2 |
| #26018326 | 2 |
| #26018214 | 2 |
| C89×#1311 | 2 |
| #12086 | 89 |