Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×C4×#13083549 | C2 | semidirect |
| 5. #26018347 | C2 | semidirect |
| 6. #26018345 | C2 | semidirect |
| 7. C89×#1945 | C2 | semidirect |
| 15. #19151401 | C4 | semidirect |
| 16. #19151398 | C4 | semidirect |
| 142. #1945 | D89 | semidirect |
| 145. C89 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151404 | 2 |
| #26021957 | 2 |
| C2×C4×#13083549 | 2 |
| #26021140 | 2 |
| #26018347 | 2 |
| #26018345 | 2 |
| C89×#1945 | 2 |
| #13151 | 89 |