Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
658 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 658 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 |
|---|---|---|
| 1. #26031174 | C2 | semidirect |
| 2. #26025205 | C2 | semidirect |
| 3. #26018934 | C2 | semidirect |
| 4. #26018747 | C2 | semidirect |
| 5. #26018643 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 110. C2×D4×C89 | SD16 | semidirect |
| 224. C89 | #10240 | semidirect |
| 313. C2×D4 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031174 | 2 |
| #26025205 | 2 |
| #26018934 | 2 |
| #26018747 | 2 |
| #26018643 | 2 |
| #26018153 | 2 |
| C89×#3036 | 2 |
| #10240 | 89 |