Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
554 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 554 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. #26018933 | C2 | semidirect |
| 5. #26018647 | C2 | semidirect |
| 6. #26018155 | C2 | semidirect |
| 7. C89×#2568 | C2 | semidirect |
| 107. C2×Q8×C89 | SD16 | semidirect |
| 206. #2568 | D89 | semidirect |
| 211. C89 | #10244 | semidirect |
| 294. C2×Q8 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031177 | 2 |
| #26029724 | 2 |
| #26018933 | 2 |
| #26018746 | 2 |
| #26018647 | 2 |
| #26018155 | 2 |
| C89×#2568 | 2 |
| #10244 | 89 |